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Estimation, recognition, and near-future prediction of 3D trajectories based on their two dimensional projections available from one camera source is an exceptionally difficult problem due to uncertainty in the trajectories and environment, high dimensionality of the specific trajectory states, lack of enough labeled data and so on. In this article, we propose a solution to solve this problem based on a novel deep learning model dubbed Disjunctive Factored Four-Way Conditional Restricted Boltzmann Machine (DFFW-CRBM). Our method improves state-of-the-art deep learning techniques for high dimensional time-series modeling by introducing a novel tensor factorization capable of driving forth order Boltzmann machines to considerably lower energy levels, at no computational costs. DFFW-CRBMs are capable of accurately estimating, recognizing, and performing near-future prediction of three-dimensional trajectories from their 2D projections while requiring limited amount of labeled data. We evaluate our method on both simulated and real-world data, showing its effectiveness in predicting and classifying complex ball trajectories and human activities., Comment: Pattern Recognition, ISSN 0031-3203, Elsevier, 2017

We propose a simple method to evaluate $\alpha$-transition rates to low-lying excited states in even-even nuclei. For this a realistic $\alpha$-daughter double folding interaction is approximated by a parabola in the region where the decay process takes place. This allows us to evaluate the penetration probability analytically. The main experimental features of branching ratios to excited states are reproduced by this simple approach., Comment: 8 pages, 6 figures

Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest $k$ such that the graph is $k$-splittable into a planar graph. A $k$-split operation substitutes a vertex $v$ by at most $k$ new vertices such that each neighbor of $v$ is connected to at least one of the new vertices. We first examine the planar split thickness of complete graphs, complete bipartite graphs, multipartite graphs, bounded degree graphs, and genus-1 graphs. We then prove that it is NP-hard to recognize graphs that are $2$-splittable into a planar graph, and show that one can approximate the planar split thickness of a graph within a constant factor. If the treewidth is bounded, then we can even verify $k$-splittability in linear time, for a constant $k$.

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time., Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)

A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its endpoints. Testing whether a graph has an RVR is known to be NP-hard. In this paper, we study the problem of finding an RVR under the assumption that an embedding in the plane of the input graph is fixed and we are looking for an RVR that reflects this embedding. We show that in this case the problem can be solved in polynomial time for general embedded graphs and in linear time for 1-plane graphs (i.e., embedded graphs having at most one crossing per edge). The linear time algorithm uses a precise list of forbidden configurations, which extends the set known for straight-line drawings of 1-plane graphs. These forbidden configurations can be tested for in linear time, and so in linear time we can test whether a 1-plane graph has an RVR and either compute such a representation or report a negative witness. Finally, we discuss some extensions of our study to the case when the embedding is not fixed but the RVR can have at most one crossing per edge.

A 1-plane graph is a graph embedded in the plane such that each edge is crossed at most once. A 1-plane graph is optimal if it has maximum edge density. A red-blue edge coloring of an optimal 1-plane graph $G$ partitions the edge set of $G$ into blue edges and red edges such that no two blue edges cross each other and no two red edges cross each other. We prove the following: $(i)$ Every optimal 1-plane graph has a red-blue edge coloring such that the blue subgraph is maximal planar while the red subgraph has vertex degree at most four; this bound on the vertex degree is worst-case optimal. $(ii)$ A red-blue edge coloring may not always induce a red forest of bounded vertex degree. Applications of these results to graph augmentation and graph drawing are also discussed.

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar.

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is an L-shape, and every edge is either a horizontal or vertical segment. As a byproduct of our drawing technique, we prove that an IC-plane graph has a RAC drawing in quadratic area with at most two bends per edge.

Let $\langle G_r,G_b \rangle$ be a pair of plane $st$-graphs with the same vertex set $V$. A simultaneous visibility representation with L-shapes of $\langle G_r,G_b \rangle$ is a pair of bar visibility representations $\langle\Gamma_r,\Gamma_b\rangle$ such that, for every vertex $v \in V$, $\Gamma_r(v)$ and $\Gamma_b(v)$ are a horizontal and a vertical segment, which share an end-point. In other words, every vertex is drawn as an $L$-shape, every edge of $G_r$ is a vertical visibility segment, and every edge of $G_b$ is a horizontal visibility segment. Also, no two L-shapes intersect each other. An L-shape has four possible rotations, and we assume that each vertex is given a rotation for its L-shape as part of the input. Our main results are: (i) a characterization of those pairs of plane $st$-graphs admitting such a representation, (ii) a cubic time algorithm to recognize them, and (iii) a linear time drawing algorithm if the test is positive.

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing.

The Geiger-Nuttall (GN) law relates the partial $\alpha$-decay half-life with the energy of the escaping $\alpha$ particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: 1) the empirical coefficients that appear in the GN law have a deep physical meaning and 2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the $\alpha$ formation probability on the neutron number is not linear or constant, the GN law is broken. For the $\alpha$ decay of neutron-deficient nucleus $^{186}$Po, the difference between the experimental half-life and that predicted by the GN Law is as large as one order of magnitude., Comment: 4 pages, 5 figures, to appear in Phys. Lett. B

A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp. a subset of) the pairs of vertices whose bars have a $\epsilon$-thick vertical line connecting them that intersects at most one other bar. We explore the relation among weak (resp. strong) bar 1-visibility graphs and other nearly planar graph classes. In particular, we study their relation to 1-planar graphs, which have a drawing with at most one crossing per edge; quasi-planar graphs, which have a drawing with no three mutually crossing edges; the squares of planar 1-flow networks, which are upward digraphs with in- or out-degree at most one. Our main results are that 1-planar graphs and the (undirected) squares of planar 1-flow networks are weak bar 1-visibility graphs and that these are quasi-planar graphs.

The low-lying level schemes and electromagnetic transitions of $^{109}$Te, $^{109}$I, and the neighboring even-even nucleus $^{108}$Te, are calculated within the framework of the $SD$-pair approximation of the nuclear shell model. Good agreement is obtained between the calculated results and experimental data. The favored components of low-lying bands are discussed in the collective nucleon-pair subspace. The weak-coupling picture shown in these nuclei and its relationship with residual quadrupole-quadrupole interaction between valence protons and neutrons are analyzed., Comment: printer-friendly version, 6 figures and 5 tables, 10 pages, to be published in PRC

In machine learning, the choice of a learning algorithm that is suitable for the application domain is critical. The performance metric used to compare different algorithms must also reflect the concerns of users in the application domain under consideration. In this work, we propose a novel probability-based performance metric called Relevance Score for evaluating supervised learning algorithms. We evaluate the proposed metric through empirical analysis on a dataset gathered from an intelligent lighting pilot installation. In comparison to the commonly used Classification Accuracy metric, the Relevance Score proves to be more appropriate for a certain class of applications., Comment: To Appear at International Conference on Machine Learning and Data Mining (MLDM 2013), 14 pages, 6 figures

It is proven that every set $S$ of distinct points in the plane with cardinality $\lceil \frac{\sqrt{\log_2 n}-1}{4} \rceil$ can be a subset of the vertices of a crossing-free straight-line drawing of any planar graph with $n$ vertices. It is also proven that if $S$ is restricted to be a one-sided convex point set, its cardinality increases to $\lceil \sqrt[3]{n} \rceil$. The proofs are constructive and give rise to O(n)-time drawing algorithms. As a part of our proofs, we show that every maximal planar graph contains a large induced biconnected outerplanar graphs and a large induced outerpath (an outerplanar graph whose weak dual is a path).

A partial conservation of the seniority quantum number in $j=9/2$ shells has been found recently in a numerical application. In this paper a complete analytic proof for this problem is derived as an extension of the work by Zamick and P. Van Isacker [Phys. Rev. C 78 (2008) 044327]. We analyze the properties of the non-diagonal matrix elements with the help of the one-particle and two-particle coefficients of fractional parentage (cfp's). It is found that all non-diagonal (and the relevant diagonal) matrix elements can be re-expressed in simple ways and are proportional to certain one-particle cfp's. This remarkable occurrence of partial dynamic symmetry is the consequence of the peculiar property of the $j=9/2$ shell, where all $v=3$ and 5 states are uniquely defined., Comment: 17 pages

The seniority scheme has been shown to be extremely useful for the classification of nuclear states in semi-magic nuclei. The neutron-proton ($np$) correlation breaks the seniority symmetry in a major way. As a result, the corresponding wave function is a mixture of many components with different seniority quantum numbers. In this contribution we show that the $np$ interaction may favor a new kind of coupling in $N=Z$ nuclei, i.e., the so-called isoscalar spin-aligned $np$ pair mode. Shell model calculations reveal that the ground and low-lying yrast states of the $N = Z$ nuclei $^{92}$Pd and $^{96}$Cd may mainly be built upon such spin-aligned $np$ pairs each carrying the maximum angular momentum $J = 9$ allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region., Comment: 5 pages, 4 figues, Proceedings of the Nordic Conference on Nuclear Physics 2011. To appear in Physica Scripta T

We have adopted the multistep shell model in the complex energy plane to study nuclear excitations occurring in the continuum part of the spectrum. In this method one proceeds by solving the shell model equations in a successive manner. That is, in each step one constructs the building blocks to be used in future steps. We applied this formalism to analyze the unbound nuclei $^{12,13}$Li starting from the one-particle states in $^{10}$Li and two-particle states in $^{11}$Li. In the former case the excitations correspond to the motion of three particles partitioned as the product of a one-particle and two-particle systems. The ground state of $^{12}$Li is thus calculated to be an antibound (virtual) state. In the four-particle system $^{13}$Li the states can be constructed as the coupling of two correlated pairs. We found that there is no bound or antibound state in $^{13}$Li., Comment: 10 pages, 2 table, 3 figures, Proceedings of the Conference on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Series

Shell model calculations reveal that the ground and low-lying yrast states of the $N=Z$ nuclei $^{92}_{46}$Pd and $^{96}$Cd are mainly built upon isoscalar spin-aligned neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This mode of excitation is unique in nuclei and indicates that the spin-aligned pair has to be considered as an essential building block in nuclear structure calculations. In this contribution we will discuss this neutron-proton pair coupling scheme in detail. In particular, we will explore the competition between the normal monopole pair coupling and the spin-aligned coupling schemes. Such a coupling may be useful in elucidating the structure properties of $N=Z$ and neighboring nuclei., Comment: 10 pages, 7 figures, 1 table. Proceedings of the Conference on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Series

It is shown that the proton formation probability, extracted from experimental data corresponding to one-proton radioactivity, is divided into two regions when plotted as a function of an universal parameter. This parameter is derived from a microscopic description of the decay process. In this way we explain the systematics of proton emission half-lives. At the same time the formation probability is shown to be a useful quantity to determine the deformation property of the mother nucleus., Comment: 5 pages, 5 figues, 2 tables, printer-friendly version, submitted to Phys. Rev. C

The multistep shell model was extended recently to incorporate both neutron and proton degrees of freedom and applied to study the structure of $N=Z$ systems with four, six and eight particles [arXiv:1108.0269]. In this work we give a brief introduction to the formalism thus developed. A more detailed explanation with applications will be updated later., Comment: 10 pages, no figure, submitted to arXiv

The recently proposed spin-aligned neutron-proton pair coupling scheme is studied within a non-orthogonal basis in term of the multistep shell model. This allows us to identify simultaneously the roles played by other configurations such as the normal pairing term. The model is applied to four-, six- and eight-hole $N=Z$ nuclei below the core $^{100}$Sn., Comment: 12 pages, 3 figures and 1 table

Shell model calculations using realistic interactions reveal that the ground and low-lying yrast states of the $N=Z$ nucleus $^{92}_{46}$Pd are mainly built upon isoscalar neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This structure is different from the ones found in the ground and low-lying yrast states of all other even-even nuclei studied so far. The low-lying spectrum of excited states generated by such correlated neutron-proton pairs has two distinctive features: i) the levels are almost equidistant at low energies and ii) the transition probability $I\rightarrow I-2$ is approximately constant and strongly selective. This unique mode is shown to replace normal isovector pairing as the dominating coupling scheme in $N=Z$ nuclei approaching the doubly-magic nucleus $^{100}$Sn., Comment: 11 pages, 5 figures, version to appear in Phys. Rev. C (Rapid communication)

The general phenomenon of shell structure in atomic nuclei has been understood since the pioneering work of Goeppert-Mayer, Haxel, Jensen and Suess.They realized that the experimental evidence for nuclear magic numbers could be explained by introducing a strong spin-orbit interaction in the nuclear shell model potential. However, our detailed knowledge of nuclear forces and the mechanisms governing the structure of nuclei, in particular far from stability, is still incomplete. In nuclei with equal neutron and proton numbers ($N = Z$), the unique nature of the atomic nucleus as an object composed of two distinct types of fermions can be expressed as enhanced correlations arising between neutrons and protons occupying orbitals with the same quantum numbers. Such correlations have been predicted to favor a new type of nuclear superfluidity; isoscalar neutron-proton pairing, in addition to normal isovector pairing (see Fig. 1). Despite many experimental efforts these predictions have not been confirmed. Here, we report on the first observation of excited states in $N = Z = 46$ nucleus $^{92}$Pd. Gamma rays emitted following the $^{58}$Ni($^{36}$Ar,2$n$)$^{92}$Pd fusion-evaporation reaction were identified using a combination of state-of-the-art high-resolution {\gamma}-ray, charged-particle and neutron detector systems. Our results reveal evidence for a spin-aligned, isoscalar neutron-proton coupling scheme, different from the previous prediction. We suggest that this coupling scheme replaces normal superfluidity (characterized by seniority coupling) in the ground and low-lying excited states of the heaviest N = Z nuclei. The strong isoscalar neutron- proton correlations in these $N = Z$ nuclei are predicted to have a considerable impact on their level structures, and to influence the dynamics of the stellar rapid proton capture nucleosynthesis process., Comment: 13 pages, 3 figures

In a previous paper we introduced a method called augmented sparse reconstruction (ASR) that identifies links among nodes of ordinary differential equation networks, given a small set of observed trajectories with various initial conditions. The main purpose of that technique was to reconstruct intracellular protein signaling networks. In this paper we show that a recursive augmented sparse reconstruction generates artificial networks that are homologous to a large, reference network, in the sense that kinase inhibition of several reactions in the network alters the trajectories of a sizable number of proteins in comparable ways for reference and reconstructed networks. We show this result using a large in-silico model of the epidermal growth factor receptor (EGF-R) driven signaling cascade to generate the data used in the reconstruction algorithm. The most significant consequence of this observed homology is that a nearly optimal combinatorial dosage of kinase inhibitors can be inferred, for many nodes, from the reconstructed network, a result potentially useful for a variety of applications in personalized medicine., Comment: 33 pages, 6 figures