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We study Néron models of pseudo-Abelian varieties over excellent discrete valuation rings of equal characteristic p > 0 and generalise the notions of good reduction and semi- Abelian reduction to such algebraic groups. We prove that the well-known representationtheoretic criteria for good and semi-Abelian reduction due to Néron--Ogg--Shafarevich and Grothendieck carry over to the pseudo-Abelian case, and give examples to show that our results are the best possible in most cases. Finally, we study the order of the group scheme of connected components of the Néron model in the pseudo-Abelian case. Our method is able to control the Ι-part (for Ι ≠ p) of this order completely, and we study the p-part in a particular (but still reasonably general) situation. [ABSTRACT FROM AUTHOR]

Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$ , and $\mathfrak {m}$ a modulus on $X$ , given by a closed subscheme of $X$ which is geometrically reduced. The generalized Jacobian $J_\mathfrak {m}$ of $X$ with respect to $\mathfrak {m}$ is then an extension of the Jacobian of $X$ by a torus. We describe its Néron model, together with the character and component groups of the special fibre, in terms of a regular model of $X$ over $R$. This generalizes Raynaud's well-known description for the usual Jacobian. We also give some computations for generalized Jacobians of modular curves $X_0(N)$ with moduli supported on the cusps. [ABSTRACT FROM AUTHOR]

Let Z be a nondegenerate hypersurface in a d-dimensional torus (C*)d defined by a Laurent polynomial f with a d-dimensional Newton polytope P. The subset F(P) ⊂ P consisting of all points in P having integral distance at least 1 to all integral supporting hyperplanes of P is called the Fine interior of P. If F(P) ≠ ∅, we construct a unique projective model Z of Z having at worst canonical singularities and obtain minimal models Z of Z by crepant morphisms b Z → Z. We show that the Kodaira dimension κ = κ(Z) equals min{d - 1, dim F(P)} and the general fibers in the Iitaka fibration of the canonical model Z are nondegenerate (d - 1 - ΰ)-dimensional toric hypersurfaces of Kodaira dimension 0. Using F(P), we obtain a simple combinatorial formula for the intersection number (KZ)d-1. [ABSTRACT FROM AUTHOR]

Minimal Model (MM) is the top-scoring model for assessing physiological characteristics to diagnose the potential or onset of type 2 diabetes mellitus (T2DM) through the intravenous glucose tolerance test (IVGTT) for the past four decades. Nevertheless it has been arguable that MM method either overestimates glucose effectiveness (GE) or underestimates insulin sensitivity (IS) in some cases by both biologists through in vivo experiments and mathematicians by analysis and/or simulations. We propose a novel model including the interstitial insulin according to physiology and adapted from the well accepted Sturis' model for the glucose-insulin metabolic system suitable to the IVGTT setting. Our model consistently overcomes the aforementioned defects in a subgroup of subjects. In addition, the variable X for insulin action in MM might be appropriately interpreted as an increment of insulin in the interstitial space in response to the bolus stimulus, rather than being proportional to the interstitial insulin as believed. [ABSTRACT FROM AUTHOR]

We work with a smooth relative curve XU/U with nodal reduction over an excellent and locally factorial scheme S. We show that blowing up a nodal model of XU in the ideal sheaf of a section yields a new nodal model and describe how these models relate to each other. We construct a Néron model for the Jacobian of XU and describe it locally on S as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the Néron model to be separated. [ABSTRACT FROM AUTHOR]

Let π 1 : X → Δ be a flat family of smooth, projective curves of genus g ≥ 2 , degenerating to an irreducible nodal curve X 0 with exactly one node. Fix an invertible sheaf L on X of relative odd degree. Let π 2 : G (2 , L) → Δ be the relative Gieseker moduli space of rank 2 semi-stable vector bundles with determinant L over X . Since π 2 is smooth over Δ ∗ , there exists a canonical family ρ ~ i : J G (2 , L) Δ ∗ i → Δ ∗ of i-th intermediate Jacobians i.e., for all t ∈ Δ ∗ , (ρ ~ i) - 1 (t) is the i-th intermediate Jacobian of π 2 - 1 (t) . There exist different Néron models ρ ¯ i : J ¯ G (2 , L) i → Δ extending ρ ~ i to the entire disc Δ , constructed by Clemens, Saito, Schnell, Zucker and Green–Griffiths–Kerr. In this article, we prove that in our setup, the Néron model ρ ¯ i is canonical in the sense that the different Néron models coincide and is an analytic fiber space which graphs admissible normal functions. We also show that for 1 ≤ i ≤ max { 2 , g - 1 } , the central fiber of ρ ¯ i is a fibration over product of copies of J k (Jac (X ~ 0)) for certain values of k, where X ~ 0 is the normalization of X 0 . In particular, for g ≥ 5 and i = 2 , 3 , 4 , the central fiber of ρ ¯ i is a semi-abelian variety. Furthermore, we prove that the i-th generalized intermediate Jacobian of the (singular) central fibre of π 2 is a fibration over the central fibre of the Néron model J ¯ G (2 , L) i . In fact, for i = 2 the fibration is an isomorphism. [ABSTRACT FROM AUTHOR]

Biofilms are composed of microorganisms attached to a solid surface or floating on top of a liquid surface. They pose challenges in the field of medicine but can also have useful applications in industry. Regulation of biofilm growth is complex and still largely elusive. Oscillations are thought to be advantageous for biofilms to cope with nutrient starvation and chemical attacks. Recently, a minimal mathematical model has been employed to describe the oscillations in Bacillus subtilis biofilms. In this paper, we investigate four different modifications to that minimal model in order to better understand the oscillations in biofilms. Our first modification is towards making a gradient of metabolites from the center of the biofilm to the periphery. We find that it does not improve the model and is therefore, unnecessary. We then use realistic Michaelis-Menten kinetics to replace the highly simple mass-action kinetics for one of the reactions. Further, we use reversible reactions to mimic the diffusion in biofilms. As the final modification, we check the combined effect of using Michaelis-Menten kinetics and reversible reactions on the model behavior. We find that these two modifications alone or in combination improve the description of the biological scenario. [ABSTRACT FROM AUTHOR]

Surveys of microbial biodiversity such as the Earth Microbiome Project (EMP) and the Human Microbiome Project (HMP) have revealed robust ecological patterns across different environments. A major goal in ecology is to leverage these patterns to identify the ecological processes shaping microbial ecosystems. One promising approach is to use minimal models that can relate mechanistic assumptions at the microbe scale to community-level patterns. Here, we demonstrate the utility of this approach by showing that the Microbial Consumer Resource Model (MiCRM) – a minimal model for microbial communities with resource competition, metabolic crossfeeding and stochastic colonization – can qualitatively reproduce patterns found in survey data including compositional gradients, dissimilarity/overlap correlations, richness/harshness correlations, and nestedness of community composition. By using the MiCRM to generate synthetic data with different environmental and taxonomical structure, we show that large scale patterns in the EMP can be reproduced by considering the energetic cost of surviving in harsh environments and HMP patterns may reflect the importance of environmental filtering in shaping competition. We also show that recently discovered dissimilarity-overlap correlations in the HMP likely arise from communities that share similar environments rather than reflecting universal dynamics. We identify ecologically meaningful changes in parameters that alter or destroy each one of these patterns, suggesting new mechanistic hypotheses for further investigation. These findings highlight the promise of minimal models for microbial ecology. [ABSTRACT FROM AUTHOR]

The canonical height associated to a polarized endomorphism of a projective variety, constructed by Call and Silverman and generalizing the Néron-Tate height on a polarized abelian variety, plays an important role in the arithmetic theory of dynamical systems. We generalize this construction to polarized correspondences, prove various fundamental properties, and show how the global canonical height decomposes as an integral of a local height over the space of absolute values on the algebraic closure of the field of definition. [ABSTRACT FROM AUTHOR]

We study the Johansen-Ledoit-Sornette (JLS) model of financial market crashes (Johansen et al. in Int J Theor Appl Financ 3(2):219-255, 2000). On our view, the JLS model is a curious case from the perspective of the recent philosophy of science literature, as it is naturally construed as a “minimal model” in the sense of Batterman and Rice (Philos Sci 81(3):349-376, 2014) that nonetheless provides a causal explanation of market crashes, in the sense of Woodward’s interventionist account of causation (Woodward in Making things happen: a theory of causal explanation. Oxford University Press, Oxford, 2003). [ABSTRACT FROM AUTHOR]

We give a uniform General Neron Desingularization (GND) for one-dimensional local rings with respect to morphisms which coincide modulo a high power of the maximal ideal. The result has interesting applications in the case of Cohen-Macaulay rings. [ABSTRACT FROM AUTHOR]

In a previous work, we described the Minimal Model Program in the family of ℚ-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs ( X, Δ) when X is a projective horospherical variety. [ABSTRACT FROM AUTHOR]

In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian varieties. The effectiveness of the height jump divisor was conjectured by Hain in the more general case of variations of polarized Hodge structures of weight −1. [ABSTRACT FROM AUTHOR]

We prove that certain degenerate abelian varieties that include compactified Jacobians, namely stable semiabelic varieties, satisfy autoduality. We establish this result by proving a comparison theorem that relates the associated family of Picard schemes to the Néron model, a result of independent interest. In our proof, a key fact is that the total space of a suitable family of stable semiabelic varieties has rational singularities. [ABSTRACT FROM AUTHOR]

A classical example of Mumford gives a generically non-reduced component of the Hilbert scheme of smooth curves in [ABSTRACT FROM AUTHOR]

Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is sufficient to cause the observed anomaly. Alternatively, a minimal correction subset comprises a minimal set of reasons whose deletion is sufficient to eliminate the observed anomaly. Circumscription formalizes such preference relations by associating propositional theories with minimal models. The resulting enumeration problem is addressed here by means of a new algorithm taking advantage of unsatisfiable core analysis. Empirical evidence of the efficiency of the algorithm is given by comparing the performance of the resulting solver, circumscriptino, with hclasp, camus mcs, lbx and mcsls on the enumeration of minimal models for problems originating from practical applications. [ABSTRACT FROM AUTHOR]

Let X be a compact Kähler manifold. We show that the Kähler-Ricci flow (as well as its twisted versions) can be run from an arbitrary positive closed current with zero Lelong numbers and immediately smoothes it. [ABSTRACT FROM AUTHOR]

An algorithmic proof of General Neron Desingularization is given here for one dimensional local rings and it is implemented in Singular . Also a theorem recalling Greenberg' strong approximation theorem is presented for one dimensional local rings. [ABSTRACT FROM AUTHOR]

The scalar color octet contribution to the resonance -pair production at the LHC is calculated and analyzed by taking into account the one-loop effective two-gluon vertex. It is shown that this contribution from the scalar color octet predicted by the minimal model with the four-color quark-lepton symmetry is for = 13 TeV of about a few percent for 750 1800 GeV and can exceed 10% for 400 750 GeV. It is also pointed out that the search for the scalar octet as the resonance in the dijet mass spectra seems to be difficult because of the smallness of its one-loop effective two-gluon interaction. [ABSTRACT FROM AUTHOR]

Let be a complete discrete valuation field. Let be its ring of integers. Let be its residue field which we assume to be algebraically closed of characteristic exponent . Let be a semi-abelian variety. Let be its Néron model. The special fiber is an extension of the identity component by the group of components . We say that has split reduction if this extension is split. Whereas has always split reduction if we prove that it is no longer the case if even if is tamely ramified. If is the Jacobian variety of a smooth proper and geometrically connected curve of genus , we prove that for any tamely ramified extension of degree greater than a constant, depending on only, has split reduction. This answers some questions of Liu and Lorenzini. [ABSTRACT FROM AUTHOR]

In this paper, we explore the connections between the Minimal Model Program and the theory of Berkovich spaces. Let k be a field of characteristic zero and letX be a smooth and projective k((t))-variety with semi-ample canonical divisor. We prove that the essential skeleton of X coincides with the skeleton of any minimal dlt-model and that it is a strong deformation retract of the Berkovich analytification of X. As an application, we show that the essential skeleton of a Calabi-Yau variety over k((t)) is a pseudo-manifold. [ABSTRACT FROM AUTHOR]

We prove the abundance theorem for log canonical n-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical (n - 1)-folds. We also discuss the log minimal model program for log canonical 4-folds. [ABSTRACT FROM AUTHOR]

Let S be a Dedekind scheme with field of functions K. We show that if XK is a smooth connected proper curve of positive genus over K, then it admits a Néron model over S, i.e., a smooth separated model of finite type satisfying the usual Néron mapping property. It is given by the smooth locus of the minimal proper regular model of XK over S, as in the case of elliptic curves. When S is excellent, a similar result holds for connected smooth affine curves different from the affine line, with locally finite type Néron models. [ABSTRACT FROM AUTHOR]

We suggest an algorithm computing, in some cases, an explicit generating set for the Néron-Severi lattice of a Delsarte surface. In a few special cases, including those of Fermat surfaces and cyclic Delsarte surfaces that were previously conjectured in the literature, we show that certain "obvious" divisors do generate the lattice. The proof is based on the computation of the Alexandermodule related to a certain abelian covering. [ABSTRACT FROM AUTHOR]

We give a dynamical proof of a result of Masser and Zannier: for any a ≠ b ∊ Q{0,1}, there are only finitely many parameters t ∊ C for which points Pa = (a, √ a(a-1)(a-t)) and Pb = (b, √b(b-1)(b-t)) are both torsion on the Legendre elliptic curve Et = {y² = x(x-1)(x-t)}. Our method also gives the finiteness of parameters t where both Pa and Pb have small Néron-Tate height. A key ingredient in the proof is an arithmetic equidistribution theorem on P¹. For this, we prove two statements about the degree-4 Lattès family ft on P¹: (1) for each c ∊ C(t), the bifurcation measure μc for the pair (ft,c) has continuous potential across the singular parameters t = 0,1,∞; and (2) for distinct points a,b ∊ C \ {0,1}, the bifurcation measures μa and μb cannot coincide. Combining our methods with the result of Masser and Zannier, we extend their conclusion to points t of small height also for a,b ∊ C(t). [ABSTRACT FROM AUTHOR]

Let X ⊂ P4 be a terminal factorial quartic 3-fold. If X is non-singular, X is birationally rigid, i.e. the classical minimal model program on any terminal Q-factorial projective variety Z birational to X always terminates with X. This no longer holds when X is singular, but very few examples of non-rigid factorial quartics are known. In this article, we rst bound the local analytic type of singularities that may occur on a terminal factorial quartic hypersurface X ⊂ P4. A singular point on such a hypersurface is of type cAn (n > 1), or of type cDm (m > 4) or of type cE6; cE7 or cE8. We rst show that if (P ∊ X) is of type cAn, n is at most 7 and, if (P ∊ X) is of type cDm, m is at most 8. We then construct examples of non-rigid factorial quartic hypersurfaces whose singular loci consist (a) of a single point of type cAn for ∊ 6 n 6 7, (b) of a single point of type cDm for m = 4 or 5 and (c) of a single point of type cEk for k = 6, 7 or 8. [ABSTRACT FROM AUTHOR]

The PQ mechanism resolving the strong CP problem and the seesaw mechanism explaining the smallness of neutrino masses may be related in a way that the PQ symmetry breaking scale and the seesaw scale arise from a common origin. Depending on how the PQ symmetry and the seesaw mechanism are realized, one has different predictions on the color and electromagnetic anomalies which could be tested in the future axion dark matter search experiments. Motivated by this, we construct various PQ seesaw models which are minimally extended from the (non-) supersymmetric Standard Model and thus set up different benchmark points on the axion–photon–photon coupling in comparison with the standard KSVZ and DFSZ models. [ABSTRACT FROM AUTHOR]

We study a family of surfaces of general type that arises from the intersections of two translates of the theta divisor on a principally polarized complex abelian four-fold. In particular, we determine the Néron-Severi lattices of these surfaces and show that for a general abelian four-fold the monodromy group of the associated variation of Hodge structures is a subgroup of index at most two in the Weyl group W(E6), whereas for a Jacobian variety it degenerates to a subgroup of the symmetric group ϑ6. [ABSTRACT FROM AUTHOR]

We study a family of surfaces of general type that arises from the intersections of two translates of the theta divisor on a principally polarized complex abelian four-fold. In particular, we determine the Néron-Severi lattices of these surfaces and show that for a general abelian four-fold the monodromy group of the associated variation of Hodge structures is a subgroup of index at most two in the Weyl group W(E6), whereas for a Jacobian variety it degenerates to a subgroup of the symmetric group ϑ6. [ABSTRACT FROM AUTHOR]

We prove that any embedding of a [ABSTRACT FROM AUTHOR]

Let A be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the Néron model of A that measures the behavior of the Néron model under tame base change. We interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where A is the Jacobian of a curve C , and we give a compact explicit formula for the jumps in terms of the combinatorial reduction data of C . [ABSTRACT FROM AUTHOR]

In a recent issue of this journal, Loehle (2014) presents a “minimal model” for estimating climate sensitivity, identical to that previously published by Loehle and Scafetta (2011). The novelty in the more recent paper lies in the straightforward calculation of an estimate of transient climate response based on the model and an estimate of equilibrium climate sensitivity derived therefrom, via a flawed methodology. We demonstrate that the Loehle and Scafetta model systematically underestimates the transient climate response, due to a number of unsupportable assumptions regarding the climate system. Once the flaws in Loehle and Scafetta's model are addressed, the estimates of transient climate response and equilibrium climate sensitivity derived from the model are entirely consistent with those obtained from general circulation models, and indeed exclude the possibility of low climate sensitivity, directly contradicting the principal conclusion drawn by Loehle. Further, we present an even more parsimonious model for estimating climate sensitivity. Our model is based on observed changes in radiative forcings, and is therefore constrained by physics, unlike the Loehle model, which is little more than a curve-fitting exercise. [ABSTRACT FROM AUTHOR]

The geography of log models refers to the decomposition of the set of effective adjoint divisors into the polytopes defined by the resulting models obtained by the log minimal model program. We will describe the geography of log models in terms of the asymptotic base loci and Zariski decompositions of adjoint divisors. As an application, we prove some structure theorems on partially ample cones, thereby giving a partial answer to a question of B. Totaro. [ABSTRACT FROM AUTHOR]

We give a new proof of formality of the operad of little disks. The proof makes use of an operadic version of a simple formality criterion for commutative differential graded algebras due to Sullivan. We see that formality is a direct consequence of the fact that the Grothendieck-Teichmüller group operates on the chain operad of little disks. [ABSTRACT FROM AUTHOR]

An unconventional type of metal-insulator transition is realized in the FeSi1-xGex alloys which is driven by the magnetic instability of the paramagnetic insulator. Recently, a minimal model for this type of transition has been introduced and studied in the limit of vanishing temperature. Here we explore the finite-temperature properties of the minimal model in the mean-field approximation. We show that the predictions of the model are in qualitative agreement with experimental data on FeSi1-xGex and on FeGe under pressure. [ABSTRACT FROM AUTHOR]

Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\mathbb{Q}$-divisor, and that there is a surjective morphism $f: X\to Z$ onto a normal variety $Z$ satisfying $K_X+B\sim _{\mathbb{Q}} f^*M$ for some big $\mathbb{Q}$-divisor $M$, and the augmented base locus ${\mathbf{B}}_+(M)$ does not contain the image of any log canonical centre of $(X,B)$. We will show that $(X,B)$ has a good log minimal model. An interesting special case is when $f$ is the identity morphism. [ABSTRACT FROM AUTHOR]

For any admissible normal function over any dimensional base, we construct by the method of log geometry a Néron model such that extends to a section of the model over the boundary. The model is Hausdorff and is a relative log manifold. [ABSTRACT FROM AUTHOR]

We study the free-energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple replica theory, we find metastable paraelectric states with a stability region that extends to zero temperature. The free energy of such states exhibits an essential singularity for weak compositional disorder pointing to their necessary occurrence. Ferroelectric states appear as local minima in the free energy at high temperatures and become stable below a coexistence temperature Tc. We calculate the phase diagram in the electric-field-temperature plane and find a coexistence line of the polar and nonpolar phases which ends at a critical point. First-order phase transitions are induced for fields sufficiently large to cross the region of stability of the metastable paraelectric phase. These polar and nonpolar states have distinct structure factors from those of conventional ferroelectrics. We use this theoretical framework to compare and gain physical understanding of various experimental results in typical relaxors. [ABSTRACT FROM AUTHOR]

We prove that every projective kawamata log terminal pair with maximal Albanese dimension has a good minimal model. We also give an affirmative answer to Ueno's problem on subvarieties of Abelian varieties. [ABSTRACT FROM AUTHOR]

We prove an extension theorem for effective purely log-terminal pairs ( X, S + B) of non-negative Kodaira dimension $${\kappa (K_X+S+B)\ge 0}$$ . The main new ingredient is a refinement of the Ohsawa-Takegoshi L extension theorem involving singular Hermitian metrics. [ABSTRACT FROM AUTHOR]

Let $(X,D)$ be a dlt pair, where $X$ is a normal projective variety. We show that any smooth family of canonically polarized varieties over $X\setminus \,{\rm Supp}\lfloor D \rfloor $ is isotrivial if the divisor $-(K_X+D)$ is ample. This result extends results of Viehweg–Zuo and Kebekus–Kovács. To prove this result we show that any extremal ray of the moving cone is generated by a family of curves, and these curves are contracted after a certain run of the minimal model program. In the log Fano case, this generalizes a theorem by Araujo from the klt to the dlt case. In order to run the minimal model program, we have to switch to a $\mathbb Q$-factorialization of $X$. As $\mathbb Q$-factorializations are generally not unique, we use flops to pass from one $\mathbb Q$-factorialization to another, proving the existence of a $\mathbb Q$-factorialization suitable for our purposes. [ABSTRACT FROM PUBLISHER]

We prove that the universal cover of a normal projective variety X is quasi-projective iff a finite étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber. [ABSTRACT FROM AUTHOR]

Let (X, L) be a quasi-polarized pair, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles KX + rL for high rational numbers r. For this we run a Minimal Model Program with scaling relative to the divisor KX + rL. We give then some applications, namely the classification up to birational equivalence of quasi-polarized pairs with sectional genus 0, 1 and of embedded projective varieties X ⊂ ℙN with degree smaller than 2 ℙN(X) + 2. [ABSTRACT FROM AUTHOR]

We analytically compute the Renyi entropies for the RSOS models, representing a wide class of exactly solvable models with multicritical conformal points described by unitary minimal models and ℤn parafermions. The exact expressions allow for an explicit comparison of the expansions around the critical points with the predictions coming from field theory. In this way, it is possible to point out the nature of the so-called "unusual corrections," clarifying the link with the operator content, the role of the symmetries and the boundary conditions. By choosing different boundary conditions, we can single out the ground states as well as certain combinations of high-energy states. We find that the entanglement spectrum is given by operators different from those responsible for the off-critical perturbation, although they belong to the same representation of a Virasoro algebra. In the parafermionic case, we observe unexpected logarithmic corrections. [ABSTRACT FROM AUTHOR]