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Nucleosynthetic isotope variations are powerful tools to investigate genetic relationships between meteorite groups and planets. They are instrumental to assess the early evolution of the solar system, including mixing and reservoir formation in the protoplanetary disk, as well as planet formation. To address these questions, we report high-precision nucleosynthetic Ti isotope compositions of a wide range of bulk meteorites, partially complemented with new Cr isotope data. New Ti isotope data confirm the first order dichotomy observed between carbonaceous chondrites (CC), representing outer solar system compositions, and non-carbonaceous (NC) meteorites from the inner solar system. The data in combination with nucleosynthetic isotope data of other elements (e.g., Cr, Ca) indicate that isotopically heterogeneous reservoirs were also present as sub-reservoirs in the inner disk (NC reservoir), generating two or more clusters i.e., (i) the Vesta-like howardites-eucrites-diogenites (HEDs), mesosiderites, angrites, acapulcoites, lodranites, and brachinites and (ii) the Earth-Mars-like ordinary chondrites (OC), aubrites, enstatite chondrites (EC), winonaites, IAB silicates, rumuruti chondrites (R), Martian and terrestrial samples. These reservoirs likely represent disk substructures such as secondary gaps and ring-structures, created by spiral arms, which were emitted from the growing Jupiter and/or Saturn. The distinct isotopic compositions of these reservoirs may reflect thermal processing of material within the disk in combination with temporal isotopic variations either due to isotopically variable infalling material from a heterogeneous molecular cloud and/or thermal processing during the infall that induced such heterogeneities. Such effects were likely reinforced by thermal processing of the material within the disk itself and by physical size- and density sorting of dust caused by the giant planets, creating gaps and pressure bumps in the disk. Genetic relationships of meteorite groups and their implications on parent body formation are evaluated. New high precision Ti isotope data are consistent with that (i) CH and CB meteorites derive from a common parent body, which most likely accreted material from the same isotopic reservoir as the parent body of CR chondrites, (ii) silicates of IAB irons and winonaites originate from the same parent body, and (iii) mesosiderites and HED meteorites have a common origin on Vesta. The indistinguishable Ti and Cr isotope compositions of HEDs/mesosiderites to acapulcoites are not attributed to a common parent body, because of petrologic and chemical differences in addition to their distinct O isotope compositions. Their parent bodies likely accreted in the same disk region, which showed a higher level of O isotope heterogeneity compared to that of Ti, Cr and other refractory nucleosynthetic tracers. The similarity in Ti isotope compositions of Martian meteorites and OCs indicates that OC-like material belongs to the main building blocks of Mars. [ABSTRACT FROM AUTHOR]

Holant ⁎ (f) denotes a class of counting problems specified by a constraint function f. We prove complexity dichotomy theorems for Holant ⁎ (f) in two settings: (1) f is any symmetric arity-3 real-valued function on input of domain size 3. (2) f is any symmetric arity-3 { 0 , 1 } -valued function on input of domain size 4. [ABSTRACT FROM AUTHOR]

The (Perfect) Matching Cut problem is to decide if a graph G has a (perfect) matching cut, i.e., a (perfect) matching that is also an edge cut of G. Both Matching Cut and Perfect Matching Cut are known to be NP -complete. A perfect matching cut is also a matching cut with maximum number of edges. To increase our understanding of the relationship between the two problems, we perform a complexity study for the Maximum Matching Cut problem, which is to determine a largest matching cut in a graph. Our results yield full dichotomies of Maximum Matching Cut for graphs of bounded diameter, bounded radius and H -free graphs. A disconnected perfect matching of a graph G is a perfect matching that contains a matching cut of G. We also show how our new techniques can be used for finding a disconnected perfect matching with a largest matching cut for special graph classes. In this way we can prove that the decision problem Disconnected Perfect Matching is polynomial-time solvable for (P 6 + s P 2) -free graphs for every s ≥ 0 , extending a known result for P 5 -free graphs (Bouquet and Picouleau, 2020). [ABSTRACT FROM AUTHOR]

• The proposed method can quickly reduce the original search range of the focusing plane by search region segmentation and solving the system of inequality equations. • The proposed method quickly detects the focusing plane by the dichotomy method with non-fixed step size. • The proposed method significantly improves the computational efficiency with guaranteed detection accuracy of the focusing plane. Autofocusing is a critical step in digital holography for reconstructing high-quality intensity and phase information, especially for the dynamic detection of moving objects. Some commonly used autofocusing methods in digital holography are time-consuming as they search over a large range to find a unique reconstruction distance. In this study, we propose a new fast autofocusing method based on search region segmentation and dichotomy. First, a new search region is obtained by segmenting the original region and solving a system of inequality equations. Second, improving the focusing evaluation function and combining this function with the dichotomy method transforms the discriminating minimum of the evaluation function into the detection of the zero-crossing position, reducing the number of searches required for the autofocusing method. The effectiveness of the proposed autofocusing method is validated through numerical simulations and experiments. The proposed method can significantly improve computational efficiency while guaranteeing the detection accuracy of the focusing plane compared with conventional methods. [ABSTRACT FROM AUTHOR]

• The rooted art-economy dichotomy does not explain the complexity of artistic activity. • The notion of posture challenges the dichotomy between art and economy. • Artists adopt a multiplicity of postures in today's conditions of cultural production. • A taxonomy of artists' postures conceptualizes the diversity of artists' trajectories. • A taxonomy of artists' postures conceptualizes the complexity of artistic activity. The rooted dichotomy between art and economy tends to simplify our understanding of the conditions under which makers of cultural products operate. The contingencies of the last decades, leading to a greater plurality of artists' practices, urge us to create new conceptual tools to seize the effective cultural production structures. This paper aims to open this dichotomy - anchored in institutional sociology, creative economy, arts management and cultural entrepreneurship - and to reveal the relational complexity of cultural production. Building on a meta-study of a body of qualitative research published between 2012 and 2022 based on semi-directed interviews, focus groups and case studies about artists' effective practices in music, performing arts, visual and mediatic arts from underground scenes or marginal communities, we identify 20 postures adopted by artists. We place these postures on two axes reflecting the intensity of economic and artistic logics. This taxonomy explains more accurately today's conditions of cultural production. It allows us to better understand: the multiplicity of artists' and works' trajectories, as well as creation networks; the coexistence and co-dependency of postures within the same practice; and the diversity of artists' practices beyond a disciplinary logic and a linear conception of artistic career. [ABSTRACT FROM AUTHOR]

The complexity of the list homomorphism problem for signed graphs appears difficult to classify. Existing results focus on special classes of signed graphs, such as trees [4] and reflexive signed graphs [25]. Irreflexive signed graphs are in a certain sense the heart of the problem, as noted by a recent paper of Kim and Siggers. We focus on a special class of irreflexive signed graphs, namely those in which the unicoloured edges form a spanning path or cycle, which we call separable signed graphs. We classify the complexity of list homomorphisms to these separable signed graphs; we believe that these signed graphs will play an important role for the general resolution of the irreflexive case. We also relate our results to a conjecture of Kim and Siggers concerning the special case of semi-balanced irreflexive signed graphs; we have proved the conjecture in another paper, and the present results add structural information to that topic. [ABSTRACT FROM AUTHOR]

Starting with the dichotomous view of Kraepelin, schizophrenia and bipolar disorder have traditionally been considered as separate entities. More recent, this taxonomic view of illnesses has been challenged and a continuum psychosis has been postulated based on genetic and neurobiological findings suggestive of a large overlap between disorders. In this paper we will review clinical and experimental data from genetics, morphology, phenomenology and illness progression demonstrating what makes schizophrenia and bipolar disorder different conditions, challenging the idea of the obsolescence of the categorical approach. However, perhaps it is also time to move beyond DSM and search for more refined clinical descriptions that could uncover clinical invariants matching better with molecular data. In the future, computational psychiatry employing artificial intelligence and machine learning might provide us a tool to overcome the gap between clinical descriptions (phenomenology) and neurobiology. [ABSTRACT FROM AUTHOR]

Correspondence homomorphisms generalize standard homomorphisms as well as correspondence colourings (also known as DP-colourings). For a fixed target graph H , we study the problem of deciding whether an input graph G , with each edge labelled by a pair of permutations of V (H) , admits a homomorphism to H 'corresponding' to the labels. Homomorphisms to H are called H -colourings, and we employ the similar term correspondence H -colourings for correspondence homomorphisms to H. We classify the complexity of this problem as a function of the fixed graph H. It turns out that there is dichotomy — each of the problems is polynomial-time solvable or NP-complete. While most graphs H yield NP-complete problems, there are interesting cases of graphs H for which the problem can be solved in polynomial time by Gaussian elimination. We also classify the complexity of the analogous correspondence list homomorphism problems, and also the complexity of a bipartite version of both problems. We give detailed proofs for the case when H is reflexive, and, for the record, sketch the remaining proofs. [ABSTRACT FROM AUTHOR]

Given a connected graph G and a terminal set R ⊆ V (G) , the Steiner tree problem (STREE) asks for a tree that includes all of R with at most r vertices from V (G) ∖ R , for some integer r ≥ 0. It is known from (Garey et al., 1977) that STREE is NP-complete in general graphs. A Split graph is a graph which can be partitioned into a clique and an independent set. White et al. (1985) have established that STREE in split graphs is NP-complete. In this paper, we present an interesting dichotomy: we show that STREE on K 1 , 4 -free split graphs is polynomial-time solvable, whereas STREE on K 1 , 5 -free split graphs is NP-complete. We investigate K 1 , 4 -free and K 1 , 3 -free (also known as claw-free) split graphs from a structural perspective. Further, using our structural study, we present polynomial-time algorithms for STREE in K 1 , 4 -free and K 1 , 3 -free split graphs. Although, polynomial-time solvability of K 1 , 3 -free split graphs is implied from K 1 , 4 -free split graphs, we wish to highlight our structural observations on K 1 , 3 -free split graphs which may be of use in solving other combinatorial problems. [ABSTRACT FROM AUTHOR]

A track control method is proposed to solve the problem of manual steering difficulties in narrow and curved sections. The performance of a ship heading controller is affected by various factors, such as delay of the ship steering gear, external environmental disturbances, and variations in ship's speed. Firstly, a Smith optimal PID heading controller is designed. Then, a speed control method based on dichotomous method is proposed to accurately control ship speed and improve the rudder efficiency. Finally, a track control method based on model prediction and feedback compensation is proposed, considering the coupling relationship between course control and speed control. The Lantang Channel is selected as the experimental water area, and comparative simulation experiments are carried out under static water and environmental disturbance. The pre-planned route information is taken as input, and the target course at the current moment is calculated by the guidance method. The target course is used as the input of the course controller to calculate the rudder angle to control the ship's motion, and the new ship position is compared with the planned route information. The above steps are repeated to track the planned route. In order to make the ship pass the curve smoothly, the target speed of the control point is preset according to the sailing convention of decelerating first and accelerating later, and the variable speed time point and variable telegraph are solved by the dichotomy. The results are as follows: (1) The maximum track deviation and speed deviation of the Smith-OP PID are 2 m and 0.21 kn, respectively, without considering environmental interference. The maximum track deviation of the traditional PID is 8 m. (2) The maximum track deviation and speed deviation of the Smith-OP PID are 25 m and 0.27 kn, respectively, under the set environmental interference. The maximum track deviation of the traditional PID is 49 m. (3) The track control method is consistent with the practical practices of "deceleration before acceleration" and "hanging high and taking low". In summary, the track control method can be well applied to narrow and curved sections, and provide a theoretical basis for subsequent research on autonomous navigation and intelligent ships. [ABSTRACT FROM AUTHOR]

Dignity is one of those human values, which have dramatically changed in the last few decades. This paper tries to raise awareness of the risks of massively used inventions and new technologies and their possibility to threaten human dignity. It briefly introduces the technologies that symbolize the new era by explaining their birth, current applications, benefits and challenges, and examines the decisive factors that might compromise human rights. Human dignity is concisely re-evaluated, paying attention to the consequences of the technologies that have already intensively modified the world we once knew. At the end, the paper offers some suggestions on how to make the future world better and more dignified. • Technologies symbolizing the new era significantly influence human values, human rights, and human dignity. • Their pervasiveness might endanger not only the end users, but also the whole humanity. • Mindful application of new inventions with higher awareness of the risks they might impose is the road to a better world. [ABSTRACT FROM AUTHOR]

Abstract We provide, for each non-self dual Borel class Γ , a concrete finite antichain basis for the class of non-potentially Γ Borel relations whose closure has an acyclic symmetrization, considering the quasi-order of injective continuous reducibility. Along similar lines, we provide a sufficient condition for reducing the oriented graph G 0 involved in the Kechris–Solecki–Todorčević dichotomy. We also prove a similar result giving a minimum set instead of an antichain if we allow rectangular reductions. [ABSTRACT FROM AUTHOR]

Abstract In a recent paper (Mérida-Angulo and Thas, 2017), the authors introduced a map F which associates a Deitmar constructible set (which is defined over the field with one element, denoted by F 1) with any given loose graph Γ. By base extension, a constructible set X k = F (Γ) ⊗ F 1 k over any field k arises. In the present paper, we will show that all these mappings are functors, and we will use this fact to study automorphism groups of the constructible sets X k. Several automorphism groups are considered: combinatorial, topological and also groups induced by automorphisms of the ambient projective space. When Γ is a finite tree, we will give a precise description of the combinatorial and projective groups, amongst other results. [ABSTRACT FROM AUTHOR]

Holant problem is a framework to study counting problems, which is expressive enough to contain Counting Graph Homomorphisms (#GH) and Counting Constraint Satisfaction Problems (#CSP) as special cases. In the present paper, we classify the computational complexity of Holant problems on 3-regular graphs, where the signature is complex valued and not necessarily symmetric. In details, we prove that Holant problem on 3-regular graphs is #P-hard except for the signature is not genuinely entangled, A -transformable, P -transformable or vanishing, in which cases the problem is tractable. [ABSTRACT FROM AUTHOR]

The article is devoted to analysis of emergent properties of the system of binary oppositions in the genetic code ensemble. The epochal model of the double helix of DNA by Watson and Crick showed that the multiple reproduction of genetic information on DNA strands uses the ancient principle "like begets like" based on the simple complementarity in pairs of nucleobases. Each of these pairs is built on the binary opposition "purine-pyrimidine". But the system of DNA n -plet alphabets and genetic coding is much richer in types of binary oppositions, which also have some coding meanings related to this principle. The article contains the results of the application of the author's "method of hierarchy binary stochastics" (HBS-method) to the analysis of the quasi-stochastic organization of binary sequences of hydrogen bonds in genomic single-stranded DNAs. This analysis revealed hidden probability rules related to dichotomous fractal-like probability trees. The relationship between inherited bodily dichotomies in living organisms and the discovered probability dichotomies in information sequences of genomic DNAs is discussed. The encoding properties of molecular binary oppositions in the DNA nucleotide system allows the algorithmic construction of (2 n ∗2 n )-matrices of probabilities of n -plets in these binary sequences, which are matrix representations of 2 n -dimensional hyperbolic numbers. Connections of these multidimensional numbers with some inherited physiological phenomena and deep neural networks are noted. A unified algebra-numeric certification of the DNAs of genomes and genes - based on these multidimensional numerical systems - is proposed. [ABSTRACT FROM AUTHOR]

Highlights • Typical contact angle algorithms for inclined plane are systematically compared. • Simplified model-based algorithms introduce significant error in some cases. • Bond number can be rapidly and accurately predicted by determined parameter. • Drop apex can be accurately evaluated by ellipse fitting algorithm. • Exact model-based algorithm can accurately get contact angle within whole range. Abstract It is hard to accurately evaluate advancing and receding contact angles for drop on inclined surface. Different from existing simplified model-based algorithms, an exact model-based dynamic contact angle algorithm is proposed. A large number of drop profiles on inclined surface with contact angle, inclination angle and Bond number within the nearly whole application range are numerically generated. After systematic investigations, the parameter closely related to Bond number is determined and the Bond number can be predicted relatively accurately and rapid. Thereafter, the Bond number is adjusted according to the dichotomy and the influence of Bond number on drop shape. The methods for determination of drop apex and scale factor of image are presented. By combining the aforementioned methods the exact model-based dynamic contact angle algorithm for drop on inclined surface is proposed. The extensively used dynamic contact angle algorithms and the proposed algorithm are used to hydrophobicity measurement for real drop image and numerical drop profile on inclined surface. The results reveal that: only the proposed algorithm can accurately evaluate dynamic contact angle without any limitation on contact angle, drop volume and inclination angle, and at the same time the exact fitted edge can be presented. [ABSTRACT FROM AUTHOR]

In this paper, we discuss and answer the following dichotomy problems: Let S be a network and Δ p , ω be a discrete p -Laplace operator with 1 < p < ∞ . (i) If u , v are functions satisfying − Δ p , ω u x ≤ − Δ p , ω v x , x ∈ S , u z ≤ v z , z ∈ ∂ S , then either u ≡ v on S ¯ or u < v in S . (ii) If u , v are functions satisfying u t x , t − Δ p , ω u x , t ≤ v t x , t − Δ p , ω v x , t , x , t ∈ S × 0 , T , u x , 0 ≤ v x , 0 , x ∈ S , u z , t ≤ v z , t , z , t ∈ ∂ S × 0 , T then either u ≡ v on S ¯ or u < v in S × ( 0 , T ) . We believe that this work is not only interesting in itself, but also gives a clue to solve the problems defined on the continuous domain. [ABSTRACT FROM AUTHOR]

In ptychography, the precise axial distance between the sample and the detector is of vital importance to retrieve the tested object with high quality, but the axial distance error cannot be entirely eliminated in the practical experiments. An autofocusing strategy based on dichotomy is proposed to rapidly correct the axial distance error. In this strategy, the total variation function that is valid for both amplitude- and phase-modulating specimens is applied to determine whether the current distance is smaller or larger than the true distance. Further, the dichotomy is used to exponentially shrink the step-size of the correction by iterative computations, which means that for the early iterations large modified step-size is used and for later iterations only small step-size is considered. Therefore, the dichotomy is beneficial to quickly confirm the accurate axial distance with few computations. Simulations and experiments are conducted to demonstrate that our proposed strategy, based on the extended ptychographic iterative engine (ePIE), is capable of calibrating the sample–detector distance with high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Correspondence homomorphisms are a common generalization of homomorphisms and of correspondence colourings. For a fixed reflexive target graph H , the problem is to decide whether an input graph G , with each edge labeled by a pair of permutations of V ( H ), admits a homomorphism to H ‘corresponding’ to the labels. We classify the complexity of this problem as a function of H . It turns out that there is dichotomy—each of the problems is polynomial or NP-complete. While most graphs H yield NP-complete problems, there is an interesting polynomial case when the problem can be solved by Gaussian elimination. We also classify the complexity of the analogous correspondence list homomorphism problems. [ABSTRACT FROM AUTHOR]

A tropical graph ( H , c ) consists of a graph H and a (not necessarily proper) vertex-colouring c of H . Given two tropical graphs ( G , c 1 ) and ( H , c ) , a homomorphism of ( G , c 1 ) to ( H , c ) is a standard graph homomorphism of G to H that also preserves the vertex-colours. We initiate the study of the computational complexity of tropical graph homomorphism problems. We consider two settings. First, when the tropical graph ( H , c ) is fixed; this is a problem called ( H , c ) - Colouring . Second, when the colouring of H is part of the input; the associated decision problem is called H - Tropical-Colouring . Each ( H , c ) - Colouring problem is a constraint satisfaction problem (CSP), and we show that a complexity dichotomy for the class of ( H , c ) - Colouring problems holds if and only if the Feder–Vardi Dichotomy Conjecture for CSPs is true. This implies that ( H , c ) - Colouring problems form a rich class of decision problems. On the other hand, we were successful in classifying the complexity of at least certain classes of H - Tropical-Colouring problems. [ABSTRACT FROM AUTHOR]

A computational problem exhibits a “gap property” when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the complexity of possible NP -hard gaps in the case of Boolean domains. As a consequence, we obtain a number of dichotomies for the complexity of specific variants of the constraint satisfaction problem: all are either polynomial-time tractable or NP -complete. Schaefer's original dichotomy for SAT variants is a notable particular case. Universal algebraic methods have been central to recent efforts in classifying the complexity of constraint satisfaction problems. A second contribution of the article is to develop aspects of the algebraic approach in the context of a number of variants of the constraint satisfaction problem. In particular, this allows us to lift our results on Boolean domains to many templates on non-Boolean domains. [ABSTRACT FROM AUTHOR]

We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph (G , σ) , equipped with lists L (v) ⊆ V (H) , v ∈ V (G) , of allowed images, to a fixed target signed graph (H , π). The complexity of the similar homomorphism problem without lists (corresponding to all lists being L (v) = V (H)) has been previously classified by Brewster and Siggers, but the list version remains open and appears difficult. We illustrate this difficulty by classifying the complexity of the problem when H is a tree (with possible loops). The tools we develop will be useful for classifications of other classes of signed graphs, and in a future companion paper we will illustrate this by using them to classify the complexity for certain irreflexive signed graphs. The structure of the signed trees in the polynomial cases is interesting, suggesting that the class of general signed graphs for which the problems are polynomial may have nice structure, analogous to the so-called bi-arc graphs (which characterised the polynomial cases of list homomorphisms to unsigned graphs). [ABSTRACT FROM AUTHOR]

Denote by Z + the set of all nonnegative integer numbers. Let A n be an m × m invertible q -periodic complex matrix, for all n ∈ Z + and some positive integers m and q . First we prove that the discrete problem ( A n ) x n + 1 = A n x n , x n ∈ C m is Hyers–Ulam stable if and only if the monodromy matrix T q associated to the family A = { A n } n ∈ Z + possesses a discrete dichotomy. Let ( a n ) , ( b n ) be complex valued 2-periodic sequences. Consider the non-autonomous recurrence ( a n , b n ) z n + 2 = a n z n + 1 + b n z n , n ∈ Z + , z n ∈ C and the matrix A n = ( 1 1 a n + b n − 1 a n − 1 ) , n ∈ Z + . We prove that the recurrence ( a n , b n ) is Hyers–Ulam stable if and only if the monodromy matrix T 2 : = A 1 A 0 has no eigenvalues on the unit circle. [ABSTRACT FROM AUTHOR]

Let p and q be positive integers with p / q ≥ 2. The "reconfiguration problem" for circular colourings asks, given two (p, q) -colourings f and g of a graph G, is it possible to transform f into g by changing the colour of one vertex at a time such that every intermediate mapping is a (p, q) -colouring? We show that this problem can be solved in polynomial time for 2 ≤ p / q < 4 and that it is PSPACE-complete for p / q ≥ 4. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings. As an application of the reconfiguration algorithm, we show that graphs with fewer than (k − 1) ! / 2 cycles of length divisible by k are k-colourable. [ABSTRACT FROM AUTHOR]

At the core of land use and governance debates in the United States are purported dualities: economy vs. environment, public goods vs. private rights, and the merits and demerits of regulation. While such dichotomies are inevitably partial, they offer a heuristic to interrogate the deeper nuances of a problem or process. I investigate these dichotomies in one site (Calaveras County, California) along the rural-urban interface (RUI). The RUI is home of some of the most valued places in contemporary society as well as some of the most challenged in terms of planning and management. Land management decisions along the RUI are complicated by social and ecological heterogeneity as well as ongoing, dynamic cultural and environmental change. Differing perspectives and shifting conditions in place influence stakeholders' views on the value and utility of a variety of resources, both environmental and social. This paper investigates how political and environmental ideologies and environmental management preferences are related in order to consider the implications of such divergent perspectives for policy and governance. Using a mixed method approach, I examine varying viewpoints related to the environment/economy dichotomy and conclude that increasing polarization of political and environmental ideals and preferences along the RUI impacts land use planning and policy as well as social, environmental, and economic outcomes. I argue that the physical and cultural landscape of the RUI is transforming and, as such, we must also (re)configure pathways for cooperation and problem solving to effectively address the challenges and contradictions of these social and ecological changes. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of Hyers–Ulam stability are generalized for non-autonomous linear differential systems. We prove that the k -periodic linear differential matrix system Z ˙ ( t ) = A ( t ) Z ( t ) , t ∈ R is Hyers–Ulam stable if and only if the matrix family L = E ( k , 0 ) has no eigenvalues on the unit circle, i.e. we study the Hyers–Ulam stability in terms of dichotomy of the differential matrix system Z ˙ ( t ) = A ( t ) Z ( t ) , t ∈ R . Furthermore, we relate Hyers–Ulam stability of the system Z ˙ ( t ) = A ( t ) Z ( t ) , t ∈ R to the boundedness of solution of the following Cauchy problem: { Y ˙ ( t ) = A ( t ) Y ( t ) + ρ ( t ) , t ≥ 0 Y ( 0 ) = x − x 0 , where A ( t ) is a square matrix for any t ∈ R , ρ ( t ) is a bounded function and x , x 0 ∈ C m . [ABSTRACT FROM AUTHOR]

Despite its prevalence, the underlying pathophysiology of dystonia remains poorly understood. Using our novel tri-component classification algorithm, extracellular neuronal activity in the globus pallidus (GP), STN, and the entopeduncular nucleus (EP) was characterized in 34 normal and 25 jaundiced dystonic Gunn rats with their heads restrained while at rest. In normal rats, neurons in each nucleus were similarly characterized by two physiologically distinct types: regular tonic with moderate discharge frequencies (mean rates in GP, STN and EP ranging from 35–41 spikes/s) or irregular at slower frequencies (17–20 spikes/s), with a paucity of burst activity. In dystonic rats, these nuclei were also characterized by two distinct principal neuronal patterns. However, in marked difference, in the dystonic rats, neurons were primarily slow and highly irregular (12–15 spikes/s) or burst predominant (14–17 spikes/s), with maintained modest differences between nuclei. In GP and EP, with increasing severity of dystonia, burstiness was moderately further increased, irregularity mildly further increased, and discharge rates mildly further reduced. In contrast, these features did not appreciably change in STN with worsening dystonia. Findings of a lack of bursting in GP, STN and EP in normal rats in an alert resting state and prominent bursting in dystonic Gunn rats suggest that cortical or other external drive is normally required for bursting in these nuclei and that spontaneous bursting, as seen in dystonia and Parkinson׳s disease, is reflective of an underlying pathophysiological state. Moreover, the extent of burstiness appears to most closely correlate with the severity of the dystonia. [ABSTRACT FROM AUTHOR]

We provide Hurewicz tests for the separation of disjoint analytic sets by rectangles of the form Γ × Γ ′ for Γ , Γ ′ ∈ { Σ 1 0 , Π 1 0 , Π 2 0 } . [ABSTRACT FROM AUTHOR]

At the United States Air Force Academy (USAFA) and many other engineering schools, the culminating experience prior to award of a degree is a capstone design experience. The desired outcomes for such a capstone design experience are very similar across engineering programs. Each program or discipline has freedom in how they achieve these outcomes, so long as it is a deliberate and traceable approach back to the desired outcomes. This freedom allows each discipline to tailor their capstone design experiences to those appropriate to their domains. When students are developed fully within a single discipline program that also offers their capstone, the structure promotes alignment of the student, instructor, and advisor expectations. However, as students are assigned outside of their core discipline to support other capstones, misunderstanding of how their unique skills support the capstone outcomes increases. The ability to then compare capstones beyond the top-level outcomes becomes difficult. This is the case for systems engineering (SE) majors at USAFA where they are allocated to other engineering capstones. In order to trace these distributed students’ capstones back to a common set of outcomes, a framework for understanding the full spectrum of their experiences is needed. This paper will review previous work in characterizing capstone experiences, present the method used to frame USAFA's capstones, and show a proposed a set of key characteristics and associated rubrics that will be used in future research. [ABSTRACT FROM AUTHOR]

Abstract: We investigate in this paper the perturbed Lyness difference equation , where are arbitrary positive real numbers and and the initial values , which is a generalization of the Lyness difference equation extensively studied. It is known that for the Lyness difference equation, i.e., the perturbed Lyness difference equation with , all its solutions are periodic or strictly oscillatory. However, one here finds that this perturbed Lyness difference equation possesses the following dichotomy: for , all of its solutions are globally asymptotically stable; for , all the sequences generated by it converge to . We hence find that there exists the essential difference for the properties of solutions between the unperturbed Lyness difference equation and the perturbed Lyness difference equation. [Copyright &y& Elsevier]

Abstract: The multicut problem with respect to the fixed pattern (di)graph Q is the following: given a (di)graph G, an integer k and a 1-1 mapping π of the vertices of Q to a subset X of ; determine whether there exists a set S of at most k edges (arcs) of G such that has no -path for every edge (arc) of Q. We first prove a dichotomy result for the complexity (they are all either polynomial or NP-complete) for multicut problems in (di)graphs in terms of the pattern Q. Then we consider a variant where the pattern is a mixed graph M; the input is a digraph D, an integer k and a 1-1 mapping π from to some subset of and the goal is to decide whether there exists a set S of at most k arcs of D that meets every -path in D for every arc of M and every -path in the underlying undirected graph of D for every edge of M. Again we prove a dichotomy result for the complexity of such mixed multicut problems in terms of the pattern M. It turns out that the only polynomial cases are those where the pattern is either a polynomial graph pattern or a polynomial digraph pattern. As soon as M contains both edges and arcs, the M -mixed cut problem becomes NP-complete. Finally, we prove that the directed feedback arc set problem is NP-complete, even in the class of digraphs which have a feedback vertex set of size 2. [Copyright &y& Elsevier]

Abstract: Interval graphs admit linear-time recognition algorithms and have several elegant forbidden structure characterizations. Interval digraphs can also be recognized in polynomial time, and they admit a characterization in terms of incidence matrices. Nevertheless, they do not have a known forbidden structure characterization or low-degree polynomial-time recognition algorithm. We introduce a new class of ‘adjusted interval digraphs’. By contrast, for these digraphs we exhibit a natural forbidden structure characterization, in terms of a novel structure which we call an ‘invertible pair’. Our characterization also yields a low-degree polynomial-time recognition algorithm of adjusted interval digraphs. It turns out that invertible pairs are also useful for undirected interval graphs, and our result yields a new forbidden structure characterization of interval graphs. In fact, it can be shown to be a natural link proving the equivalence of some known characterizations of interval graphs—the theorems of Lekkerkerker and Boland, and of Fulkerson and Gross. In addition, adjusted interval digraphs naturally arise in the context of list homomorphism problems. If is a reflexive undirected graph, the list homomorphism problem LHOM() is polynomial if is an interval graph, and NP-complete otherwise. If is a reflexive digraph, LHOM() is polynomial if is an adjusted interval graph, and we conjecture that it is also NP-complete otherwise. We show that our results imply the conjecture in two important cases. [Copyright &y& Elsevier]

Abstract: This paper focuses on the grout cohesive strength and the grout friction angle of rock bolt, which have a significant influence on the pullout force and are difficult to estimate. Traditional method estimate the two parameters from the results of pull-out test conducted under different confining pressures. St. John and Van Dillen gave two approximate empirical formulas in 1984. In this text, a new method was proposed to back calculate the grout cohesive strength and the grout friction angle based on given field pullout force of rock bolt. In order to verify the method, a numerical model was built by FLAC3D to approach the two parameters by the principle of dichotomy. The convergence result had been proved to be right by numerical pull-out tests. [Copyright &y& Elsevier]

Abstract: In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed. [Copyright &y& Elsevier]

Abstract: Spectral Change Vector Analysis (CVA) is based on multi-temporal images. In this paper, a dichotomy search which can be used on detecting changes in the threshold vector is adopted. Meanwhile, a supervised classification technique is used in the direction cosine space with the type of central point in the initial assay vector remote sensing images. Results are discussed in the last part of this paper, which show that CVA can extract change information effectively in our study area of Wuhan city. [Copyright &y& Elsevier]

Abstract: Matrix partition problems generalize graph colouring and homomorphism problems and occur frequently in the study of perfect graphs. It is difficult to decide, even for a small matrix M, whether the M-partition problem is polynomial time solvable or NP-complete (or possibly neither), and whether M-partitionable graphs can be characterized by a finite set of forbidden induced subgraphs (or perhaps some other first order condition). We discuss these problems for the class of chordal graphs. [Copyright &y& Elsevier]

Abstract: We investigate simultaneous solutions of the matrix Sylvester equations , where and are k-tuples of commuting matrices of order and , respectively. We show that the matrix Sylvester equations have a unique solution X for every compatible k-tuple of matrices if and only if the joint spectra and are disjoint. We discuss the connection between the simultaneous solutions of Sylvester equations and related questions about idempotent matrices separating disjoint subsets of the joint spectrum, spectral mapping for the differences of commuting k-tuples, and a characterization of the joint spectrum via simultaneous solutions of systems of linear equations. [Copyright &y& Elsevier]

Abstract: This article examines the dichotomies of collectivism and individualism in the debates on the selective abortion of disabled fetuses, which have occurred over the last four decades in Japan. Disagreements in debates on abortion in Japan have often revolved around the concept of self-determination (jiko-kettei). These debates usually focus on whether this ‘foreign’ concept is appropriate in a Japanese context, as the dominant Japanese discourse stereotypes the Japanese as making decisions in a harmonious manner. Both in public debates and in academic writing on abortion, the idea that the West is devoid of harmonious collectivism is often presented in an uncritical manner. In this article, we argue that the notion of ‘self-determination’ is borrowed from ‘reverse Orientalist’ and Occidentalist discourses that portray Westerners as individualistic or ego-centric and the Japanese as collectivist. The concept of ‘self-determination’ was remolded and projected onto Japanese public and academic debates on abortion. The relevance of this concept lies in the ways in which dichotomous views of ‘Japan as harmonious’ versus ‘the West as individualistic’ influence guidelines concerning prenatal testing and its daily practice. By critically analyzing the narratives of policy-makers and academic studies on self-determination and prenatal testing, this study traces these polarizing views back to the processes of national identity formation. These processes underlie political debates and academic work associated with the search for ‘Japanese-ness’. This article further demonstrates that policy-makers’ criticism of self-determination in prenatal testing derives from gender bias, which is also related to issues of Japanese identity. This article is based on both archival and field research materials collected between 1997 and 2008. We also refer to interviews with medical doctors, policy-makers, journalists, counselors, nurses, participants in various social movements and individuals undergoing prenatal testing, taken from a total of 180 interviews. [Copyright &y& Elsevier]

Abstract: Trigraph list homomorphism problems, also known as list matrix partition problems, generalize graph list colouring and digraph list homomorphism problems. While digraph list homomorphism problems enjoy a dichotomy (each problem is -complete or polynomial time solvable), such dichotomy is not necessarily expected for trigraph list homomorphism problems, and in the few cases where dichotomy has been proved, for small trigraphs, the progress has been slow. In this paper, we prove dichotomy for trigraph list homomorphism problems where the underlying graph of the trigraph is a tree. In fact, we show that for these trigraphs the trigraph list homomorphism problem is polynomially equivalent to a related digraph list homomorphism problem. The result can be extended to a larger class of trigraphs, and we illustrate the extension on trigraph cycles. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of controller design for Lur’e systems guaranteeing dichotomy is investigated. On the basis of Kalman–Yakubovich–Popov (KYP) lemma and two frequency equalities, a new methodology for the dichotomy analysis of the Lur’e systems is proposed. A linear matrix inequality (LMI) based criterion is derived, which is equivalent to the Leonov’s frequency-domain one, while for the dichotomy analysis and synthesis which is more straightforward than the frequency-domain one. In virtue of this result, a dynamic output feedback controller ensuring the dichotomy property for Lur’e systems is designed. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach. [Copyright &y& Elsevier]

Abstract: Rhizophores – leafless axial organs, which apices are the only sites for root formation – are unique to the Selaginella genus. Both rhizophores and roots are dichotomously branched, forming a multibranch rhizophore–root system. In the examined Selaginella kraussiana, the first dichotomous division of a rhizophore results in the initiation of the twin root meristems, giving rise to the root primordia. These primordia are temporarily arrested in growth, but at the same time they are elevated, hidden inside the rhizophore apex due to the activity of a meristematic zone at the rhizophore axis. This meristematic region, located basally to the root meristems, apart from the rhizophore tissues consists of the derivative cells of root primordia and may be considered as a specific intercalary meristem. The growth mode of the roots is similar to that of the rhizophore, including dichotomous branching of the meristem and a temporary developmental arrest of the subsequent root primordia. The reiteration of the developmental program also involves the formation of new intercalary zones, thus through divisional activity, the root with dichotomized apex grows for some time as a single axis and, then the young roots emerge. At each step of the rhizophore–root branch system formation, tissues of the parental axis contribute significantly to the growth and emergence of the next axes. Therefore, dichotomous branching in Selaginella appears to be exceptional in comparison with other known dichotomies of axial organs. [Copyright &y& Elsevier]

Abstract: Contact time (or link duration) is a fundamental factor that affects performance in Mobile Ad Hoc Networks. Previous research on theoretical analysis of contact time distribution for random walk models (RW) assume that the contact events can be modeled as either consecutive random walks or direct traversals, which are two extreme cases of random walk, thus with two different conclusions. In this paper we conduct a comprehensive research on this topic in the hope of bridging the gap between the two extremes. The conclusions from the two extreme cases will result in a power-law or exponential tail in the contact time distribution, respectively. However, we show that the actual distribution will vary between the two extremes: a power-law-sub-exponential dichotomy, whose transition point depends on the average flight duration. Through simulation results we show that such conclusion also applies to random waypoint. [ABSTRACT FROM AUTHOR]

Abstract: Growth characteristics and crown parameters of the evergreen, hemiparasitic mistletoe Viscum album were studied using a growth model based on the regular dichotomous growth and conservancy of branching patterns. Data were collected from one final harvest of 13 individuals of three different subspecies growing on the hosts Betula pendula, Abies alba and Pinus sylvestris. Compared to Viscum album ssp. album growing on deciduous hosts, the two subspecies abietis and austriacum (syn. laxum) on evergreen hosts showed longer average leaf life spans, but leaves continuously increased in area over time up to an age of at least 4 years irrespective of host. Relative growth rates in plant dry matter (RGR; 0.53–0.61gg−1 a−1) were in the same range as of deciduous shrubs in central Europe but clearly higher than in mature forest trees. However, this growth is hidden within the spherical crowns of mistletoes, as annual increase in crown volume is extraordinarily low, resulting in very high leaf area densities (LAD; 7.7–17.6m2 m−3), not found in any other woody species. Besides differences in leaf size and phenology, the three subspecies exhibit similar patterns of partitioning. As in other mistletoe species, significant parts of dry matter are regularly allocated into fruit production (10–15%). Regarding the generally lower net photosynthesis rates in mistletoes as compared to their hosts, it is questioned, whether photoautotrophic carbon gain of the leaves is sufficient to maintain the observed high relative growth rates. [ABSTRACT FROM AUTHOR]

Abstract: For digraphs and , a mapping is a homomorphism of to if implies . For a fixed digraph , the homomorphism problem is to decide whether an input digraph admits a homomorphism to or not, and is denoted as HOM(). An optimization version of the homomorphism problem was motivated by a real-world problem in defence logistics and was introduced in Gutin, Rafiey, Yeo and Tso (2006) . If each vertex is associated with costs , then the cost of the homomorphism is . For each fixed digraph , we have the minimum cost homomorphism problem for and denote it as MinHOM(). The problem is to decide, for an input graph with costs , whether there exists a homomorphism of to and, if one exists, to find one of minimum cost. Although a complete dichotomy classification of the complexity of MinHOM() for a digraph remains an unsolved problem, complete dichotomy classifications for MinHOM() were proved when is a semicomplete digraph Gutin, Rafiey and Yeo (2006) , and a semicomplete multipartite digraph Gutin, Rafiey and Yeo (2008) . In these studies, it is assumed that the digraph is loopless. In this paper, we present a full dichotomy classification for semicomplete digraphs with possible loops, which solves a problem in Gutin and Kim (2008) . [Copyright &y& Elsevier]

Abstract: The limit set trichotomy and dichotomy for skew-product semiflows are established under suitable monotone and concave assumptions. As an application, a delayed Hopfield-type neural network model is considered. [Copyright &y& Elsevier]

Abstract: An instance of the maximum constraint satisfaction problem (Max CSP) is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max -SAT and Max Cut) and is consequently NP-hard. Thus, it is natural to study how restrictions on the allowed constraint types (or constraint language) affect the complexity and approximability of Max CSP. The PCP theorem is equivalent to the existence of a constraint language for which Max CSP has a hard gap at location 1; i.e. it is NP-hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable. All constraint languages, for which the CSP problem (i.e., the problem of deciding whether all constraints can be satisfied) is currently known to be NP-hard, have a certain algebraic property. We prove that any constraint language with this algebraic property makes Max CSP have a hard gap at location 1 which, in particular, implies that such problems cannot have a PTAS unless . We then apply this result to Max CSP restricted to a single constraint type; this class of problems contains, for instance, Max Cut and Max DiCut. Assuming P NP, we show that such problems do not admit PTAS except in some trivial cases. Our results hold even if the number of occurrences of each variable is bounded by a constant. Finally, we give some applications of our results. [Copyright &y& Elsevier]

Abstract: We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of -transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For equations of nonconvolution type, Liapunov functions are used to find explicit criteria for stability. Moreover, the resolvent matrix is defined to produce a variation of constants formula. The study of asymptotic equivalence for difference equations with infinite delay is carried out in Section 6. Finally, we state some problems. [Copyright &y& Elsevier]

Abstract: We have proved in an earlier paper that the complexity of the list homomorphism problem, to a fixed graph , does not change when the input graphs are restricted to have bounded degrees (except in the trivial case when the bound is two). By way of contrast, we show in this paper that the extension problem, again to a fixed graph , can, in some cases, become easier for graphs with bounded degrees. [Copyright &y& Elsevier]

Abstract: Given a graph , let be the minimum integer , if it exists, for which -colouring is -complete when restricted to instances with degree bounded by . We show that exists for any non-bipartite graph. This verifies for graphs the conjecture of Feder, Hell, and Huang that any that is -complete, is -complete for instances of some maximum degree. Furthermore, we show the same for all projective s, and we get constant upper bounds on the parameter for various infinite classes of graph. For example, we show that for any graph with girth at least 7 in which every edge lies in a -cycle, where is the odd-girth of . [Copyright &y& Elsevier]

Abstract: This paper proposes a model of serpentinization of the Southern martian crust that may explain the topographic dichotomy, the absence of an associated free-air gravity anomaly and the presence of strong magnetic anomalies in the Southern Hemisphere. The thermodynamical conditions for serpentinization were likely met in the lithosphere during the Noachian period. This process may have decreased the density in the Southern crust and created the topographic dichotomy. Different reactions of serpentinization that can form magnetite have been considered. Assuming an intense magnetic field (core dynamo), we obtain chemical remanent magnetizations that are in the order of the estimates deduced from martian magnetic anomaly studies. The pertinence and the implications of our model concerning the early thermal evolution of Mars are discussed, with emphasis on the intensity of the paleo-magnetic field. [Copyright &y& Elsevier]