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We construct a cubic cut-and-join operator description for the partition function of the Chekhov–Eynard–Orantin topological recursion for a local spectral curve with simple ramification points. In particular, this class contains partition functions of all semi-simple cohomological field theories. The cut-and-join description leads to an algebraic version of topological recursion. For the same partition functions we also derive N families of the Virasoro constraints and prove that these constraints, supplemented by a deformed dimension constraint, imply the cut-and-join description. [ABSTRACT FROM AUTHOR]

The Lowest Unique Positive Integer game, a.k.a. Limbo, is among the simplest games that can be played by any number of players and has a nontrivial strategic component. Players independently pick positive integers, and the winner is the player that picks the smallest number nobody else picks. The Nash equilibrium for this game is a mixed strategy, (p (1) , p (2) , ...) , where p(k) is the probability you pick k. A recursion for the Nash equilibrium has been previously worked out in the case where the number of players is Poisson distributed, an assumption that can be justified when there is a large pool of potential players. Here, we summarize previous results and prove that as the (expected) number of players, n, goes to infinity, a properly scaled version of the Nash equilibrium random variable converges in distribution to a Unif(0, 1) random variable. The result implies that for large n, players should choose a number uniformly between 1 and ϕ n ∼ O (n / ln (n)) . Convergence to the uniform is rather slow, so we also investigate a continuous analog of the Nash equilibrium using a differential equation derived from the recursion. The resulting approximation is unexpectedly accurate and is interesting in its own right. Studying the differential equation yields some useful analytical results, including a precise expression for ϕ n , and efficient ways to sample from the continuous approximation. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]

"The Story of Proof: Logic and the History of Mathematics" by John Stillwell is a book that explores the development of mathematical proofs throughout history. The author examines the emergence of proofs in antiquity and the long-standing dominance of Euclid's foundations of geometry. Stillwell presents a historical narrative of mathematical achievements and subfields, highlighting the ways in which different areas of mathematics are interconnected. The book also discusses the influence of linguistic and conceptual developments on the evolution of mathematics, including the role of infinity and the impact of notation. While the text assumes some prior knowledge of mathematical proofs, it provides numerous examples and explanations to help readers understand the subject. The book concludes with a discussion of modern foundations of mathematics and the potential for computer-assisted proof and automated proof verification. [Extracted from the article]

We prove that the Langmann–Szabo–Zarembo (LSZ) model with quartic potential, a toy model for a quantum field theory on noncommutative spaces grasped as a complex matrix model, obeys topological recursion of Chekhov, Eynard and Orantin. By introducing two families of correlation functions, one corresponding to the meromorphic differentials ω g , n of topological recursion, we obtain Dyson–Schwinger equations that eventually lead to the abstract loop equations being, together with their pole structure, the necessary condition for topological recursion. This strategy to show the exact solvability of the LSZ model establishes another approach towards the exceptional property of integrability in some quantum field theories. We compare differences in the loop equations for the LSZ model (with complex fields) and the Grosse–Wulkenhaar model (with hermitian fields) and their consequences for the resulting particular type of topological recursion that governs the models. [ABSTRACT FROM AUTHOR]

This article presents a theory of recursion in thinking and language. In the logic of computability, a function maps one or more sets to another, and it can have a recursive definition that is semi-circular, i.e., referring in part to the function itself. Any function that is computable – and many are not – can be computed in an infinite number of distinct programs. Some of these programs are semi-circular too, but they needn't be, because repeated loops of instructions can compute any recursive function. Our theory aims to explain how naive individuals devise informal programs in natural language, and is itself implemented in a computer program that creates programs. Participants in our experiments spontaneously simulate loops of instructions in kinematic mental models. They rely on such loops to compute recursive functions for rearranging the order of cars in trains on a track with a siding. Kolmogorov complexity predicts the relative difficulty of abducing such programs – for easy rearrangements, such as reversing the order of the cars, to difficult ones, such as splitting a train in two and interleaving the two resulting halves (equivalent to a faro shuffle). This rearrangement uses both the siding and part of the track as working memories, shuffling cars between them, and so it relies on the power of a linear-bounded computer. Linguistic evidence implies that this power is more than necessary to compose the meanings of sentences in natural language from those of their grammatical constituents. [ABSTRACT FROM AUTHOR]

We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We formulate the problem in terms of off-shell fields in Poincare coordinates. This is especially convenient for conformal theories, where the static patch can be viewed as a flat causal diamond, with one tip at the origin and the other at timelike infinity. As an important example, we consider Yang-Mills theory at tree level. We find that static-patch scattering for Yang-Mills is subject to BCFW-like recursion relations. These can reduce any static-patch amplitude to one with N−1MHV helicity structure, dressed by ordinary Minkowski amplitudes. We derive all the N−1MHV static-patch amplitudes from self-dual Yang-Mills field solutions. Using the recursion relations, we then derive from these an infinite set of MHV amplitudes, with arbitrary number of external legs. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the stochastic recursion W i + 1 = [ V i W i + Y i ] + that can be interpreted as an autoregressive process of order 1, reflected at 0. We start our exposition by a discussion of the model's stability condition. Writing Y i = B i - A i , for independent sequences of nonnegative i.i.d. random variables { A i } i ∈ N 0 and { B i } i ∈ N 0 , and assuming { V i } i ∈ N 0 is an i.i.d. sequence as well (independent of { A i } i ∈ N 0 and { B i } i ∈ N 0 ), we then consider three special cases (i) V i equals a positive value a with certain probability p ∈ (0 , 1) and is negative otherwise, and both A i and B i have a rational LST, (ii) V i attains negative values only and B i has a rational LST, (iii) V i is uniformly distributed on [0, 1], and A i is exponentially distributed. In all three cases, we derive transient and stationary results, where the transient results are in terms of the transform at a geometrically distributed epoch. [ABSTRACT FROM AUTHOR]

It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some continuous and discrete integrable positive hierarchies such as the potential modified Korteweg-de Vries hierarchy, the potential Fordy-Gibbons hierarchies, the potential dispersionless Kadomtsev-Petviashvili-like (dKPL) hierarchy, the differential-difference dKPL hierarchy and the second heavenly hierarchies are converted to the integrable negative hierarchies including the sG hierarchy and the Tzitzeica hierarchy, the two-dimensional dispersionless Toda hierarchy, the two-dimensional Toda hierarchies and negative heavenly hierarchy. In (1+1)-dimensional cases the positive/negative hierarchy dualities are guaranteed by the dualities between the recursion operators and their inverses. In (2+1)-dimensional cases, the positive/negative hierarchy dualities are explicitly shown by using the formal series symmetry approach, the mastersymmetry method and the relativistic invariance of the duality relations. For the 4-dimensional heavenly system, the duality problem is studied firstly by formal series symmetry approach. Two elegant commuting recursion operators of the heavenly equation appear naturally from the formal series symmetry approach so that the duality problem can also be studied by means of the recursion operators. [ABSTRACT FROM AUTHOR]

Following Babai's algorithm (Graph isomorphism in quasipolynomial time, arXiv:1512.03547v2, 2016) for the string isomorphism problem, we determine that it is possible to write expressions of short length describing certain permutation cosets, including all permutation subgroups. This is feasible both in the original version of the algorithm and in its CFSG-free version, by Babai (2016, §13.1) and Pyber (A CFSG-free analysis of Babai's quasipolynomial GI algorithm, arXiv:1605.08266, 2016). The existence of such descriptions gives a weak form of the Cameron–Maróti classification, even without assuming CFSG. This is applicable to proofs of diameter bounds for Alt (n) as in Helfgott (Growth in linear algebraic groups and permutation groups: towards a unified perspective, arXiv:1804.03049, 2018): our main result is used in Dona (Towards a CFSG-free diameter bound for Alt (n) , arXiv:1810.02710v3, 2018) to free Helfgott's proof from the use of CFSG. We also thoroughly explicate Babai's recursion process (as given in Helfgott et al. in Graph isomorphisms in quasi-polynomial time, arXiv:1710.04574, 2017) and obtain explicit constants for the runtime of the algorithm, both with and without the use of CFSG. [ABSTRACT FROM AUTHOR]

The present work determines the arithmetic complexity of the index sets of u.c.e. families which are learnable according to various criteria of algorithmic learning. Specifically, we prove that the index set of codes for families that are TxtFex b a -learnable is Σ 4 0 -complete and that the index set of TxtFex ∗ ∗ -learnable and the index set of TxtFext ∗ ∗ -learnable families are both Σ 5 0 -complete. [ABSTRACT FROM AUTHOR]

We consider U(N) N = 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the 1 2 -BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling λ, order by order in 1/N, and then taking the λ ≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885. [ABSTRACT FROM AUTHOR]

Horizontal and vertical generating functions and recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal and vertical log-concavity of triangular sequences assigned to polynomials which show up in combinatorics, number theory and physics. This includes Laguerre polynomials, the Pochhammer polynomials, the D'Arcais and Nekrasov–Okounkov polynomials. [ABSTRACT FROM AUTHOR]

How does load and the notion of I spare servers i (see [[8]]) affect the dependence structure of HT ht ? How can we describe the dependence structure this induces on HT ht ? The study of multi-server queues (with HT ht servers) is complicated by the need to track and analyze a I k i -dimensional vector to precisely characterize performance. [Extracted from the article]

Alan brought several visitors to Buffalo, including Reuven Bar-Yehuda in 1992 and Christian Glaßer, Edith Hemaspaandra, and Mitsu Ogihara as postdocs. B Mitsunori Ogihara b Alan's friends and colleagues Graph With great sadness, we report the passing of Alan L. Selman, who left this world on January 22, 2021. Alan received his Ph.D. in Mathematics in 1970 from the Pennsylvania State University. [Extracted from the article]

The on-shell recursion relation has been recognized as a powerful tool for calculating tree-level amplitudes in quantum field theory, but it does not work well when the residue of the deformed amplitude A ^ (z) does not vanish at infinity of z. However, in such a situation, we still can get the right amplitude by computing the boundary contribution explicitly. In Arkani-Hamed and Kaplan (JHEP 04:076. 10.1088/1126-6708/2008/04/076. arXiv:0801.2385, 2008), the background field method was first used to analyze the boundary behaviors of amplitudes with two deformed external lines in different theories. The same method has been generalized to calculate the explicit boundary operators of some amplitudes with BCFW-like deformation in Jin and Feng (JHEP 04:123. 10.1007/JHEP04(2016)123. arXiv:1507.00463, 2016). In this paper, we will take a step further to generalize the method to the case of multiple-line deformation, and to show how the boundary behaviors (even the boundary contributions) can be extracted in the method. [ABSTRACT FROM AUTHOR]

We construct three nonequivalent gradings in the algebra . The first is the standard grading obtained with the Coxeter automorphism using its dihedral realization. In the second, we use , where is the mirror automorphism. The third is , where is the external automorphism of order 3. For each of these gradings, we construct a basis in the corresponding linear subspaces , the orbits of the Coxeter automorphisms, and the related Lax pairs generating the corresponding modified Korteweg–de Vries (mKdV) hierarchies. We find compact expressions for each of the hierarchies in terms of recursion operators. Finally, we write the first nontrivial mKdV equations and their Hamiltonians in explicit form. For , these are in fact two mKdV systems because the exponent 3 has the multiplicity two in this case. Each of these mKdV systems consists of four equations of third order in . For , we have a system of three equations of third order in . For , we have a system of two equations of fifth order in . [ABSTRACT FROM AUTHOR]

A new recursive algorithm is proposed for multiplying matrices of order n = 2q (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4μ with μ = 2q−1 (q > 0). As compared with the well-known recursive Strassen's and Winograd–Strassen's algorithms, the new algorithm minimizes the multiplicative complexity equal to Wm ≈ 0.932n2.807 multiplication operations at recursive level d = log2n−3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated. [ABSTRACT FROM AUTHOR]

In the EDGE BIPARTIZATION problem one is given an undirected graph G and an integer k, and the question is whether k edges can be deleted from G so that it becomes bipartite. Guo et al. (J Comput Syst Sci 72(8):1386-1396, 2006) proposed an algorithm solving this problem in time O(2k·m2); today, this algorithm is a textbook example of an application of the iterative compression technique. Despite extensive progress in the understanding of the parameterized complexity of graph separation problems in the recent years, no significant improvement upon this result has been yet reported. We present an algorithm for EDGE BIPARTIZATION that works in time O(1.977k·nm), which is the first algorithm with the running time dependence on the parameter better than 2k. To this end, we combine the general iterative compression strategy of Guo et al.  (2006), the technique proposed by Wahlström (in: Proceedings of SODA'14, SIAM, 2014) of using a polynomial-time solvable relaxation in the form of a Valued Constraint Satisfaction Problem to guide a bounded-depth branching algorithm, and an involved Measure&Conquer analysis of the recursion tree. [ABSTRACT FROM AUTHOR]

We sketch a broadening of the Gupta-Belnap notion of a circular or revision theoretic definition into that of a more generalized form incorporating ideas of Kleene's generalized or higher type recursion. This thereby connects the philosophically motivated, and derived, notion of a circular definition with an older form of definition by recursion using functionals, that is functions of functions, as oracles. We note that Gupta and Belnap's notion of 'categorical in L' can be formulated in at least one of these schemes. [ABSTRACT FROM AUTHOR]

The accurate description of contact characteristics between tire and road surface may significantly affect the vehicle motion simulation and control analysis. Based on the LuGre tire model, the pressure distribution function of loading is modified as a non-uniform distribution pattern through new method of recursion formula. The mathematical expression of modified LuGre tire model is achieved through introducing the Bouc-Wen model to reflect tire hysteresis behavior, which takes into consideration the process of dynamic effect of tire vertical loading and tire footprint length. The effectiveness of model is verified through comparison with classic magic formula (MF) and LuGre tire model. Furthermore, the stability of solution for the modified LuGre tire model in the prediction of tire force and alignment torque is demonstrated in frequency domain. Finally, a nonlinear four-DOF vehicle handling dynamics model is built. The front wheel steering angle and the rotational angular velocities of the six tire from a calibrated virtual vehicle is entered into the vehicle model system with modified LuGre tire model as input data. The responses of longitudinal velocity, lateral velocity, yaw rate and roll angle are obtained under two kinds of limit conditions. The comparison results demonstrate the correctness and effectiveness of the built model, which further prove that the modified LuGre tire model is applicable for handling performance analysis of vehicle system. [ABSTRACT FROM AUTHOR]

We study how the shelling components behave under the pyramid and prism operations. As a consequence we obtain a concise recursion for the cubical shelling contributions. [ABSTRACT FROM AUTHOR]

We introduce a construction of a set of code sequences {Cn(m) : n ≥ 1, m ≥ 1} with memory order m and code length N(n). {Cn(m)} is a generalization of polar codes presented by Arıkan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n − 1) and N(n − m), and {Cn(m)} coincides with the original polar codes when m = 1. We show that {Cn(m)} achieves the symmetric capacity I(W) of an arbitrary binary-input, discrete-output memoryless channel W for any fixed m. We also obtain an upper bound on the probability of block-decoding error Pe of {Cn(m)} and show that Pe=O(2−Nβ) is achievable for β < 1/[1+m(ϕ − 1)], where ϕ ∈ (1, 2] is the largest real root of the polynomial F(m, ρ) = ρm − ρm − 1 − 1. The encoding and decoding complexities of {Cn(m)} decrease with increasing m, which proves the existence of new polar coding schemes that have lower complexity than Arıkan's construction. [ABSTRACT FROM AUTHOR]

We study large c conformal blocks outside the known limits. This work seems to be hard, but it is possible numerically by using the Zamolodchikov recursion relation. As a result, we find new some properties of large c conformal blocks with a pair of two different dimensions for any channel and with various internal dimensions. With light intermediate states, we find a Cardy-like asymptotic formula for large c conformal blocks and also we find that the qualitative behavior of various large c blocks drastically changes when the dimensions of external primary states reach the value c=32. And we proceed to the study of blocks with heavy intermediate states hp and we find some simple dependence on heavy hp for large c blocks. The results in this paper can be applied to, for example, the calculation of OTOC or Entanglement Entropy. In the end, we comment on the application to the conformal bootstrap in large c CFTs. [ABSTRACT FROM AUTHOR]

Reversible computing is both forward and backward deterministic. This means that a uniquely determined step exists from the previous computational configuration (backward determinism) to the next one (forward determinism) and vice versa. We present the reversible primitive recursive functions (RPRF), a class of reversible (endo-)functions over natural numbers which allows to capture interesting extensional aspects of reversible computation in a formalism quite close to that of classical primitive recursive functions. The class RPRF can express bijections over integers (not only natural numbers), is expressive enough to admit an embedding of the primitive recursive functions and, of course, its evaluation is effective. We also extend RPRF to obtain a new class of functions which are effective and Turing complete, and represent all Kleene’s μ-recursive functions. Finally, we consider reversible recursion schemes that lead outside the reversible endo-functions. [ABSTRACT FROM AUTHOR]

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda τ -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers. [ABSTRACT FROM AUTHOR]

We show that Dedekind, in his proof of the principle of definition by mathematical recursion, used implicitly both the concept of an inductive cone from an inductive system of sets and that of the inductive limit of an inductive system of sets. Moreover, we show that in Dedekind’s work on the foundations of mathematics one can also find specific occurrences of various profound mathematical ideas in the fields of universal algebra, category theory, the theory of primitive recursive mappings, and set theory, which undoubtedly point towards the mathematics of twentieth and twenty-first centuries. [ABSTRACT FROM AUTHOR]

The numerical rank determination frequently occurs in matrix computation when the conventional exact rank of a hidden matrix is desired to be recovered. This paper presents a Matlab package RankRev that implements two efficient algorithms for computing the numerical rank and numerical subspaces of a matrix along with updating/downdating capabilities for making adjustment to the results when a row or column is inserted/deleted. The package and the underlying algorithms are accurate, reliable, and much more efficient than the singular value decomposition when the matrix is of low rank or low nullity. [ABSTRACT FROM AUTHOR]

In this paper, we define a new constrained multi-component KP(cMKP) hierarchy which contains the constrained KP(cKP) hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy. [ABSTRACT FROM AUTHOR]

The goal of this article is to prove that the determinantal formulas of the Painlevé 2 system identify with the correlation functions computed from the topological recursion on their spectral curve for an arbitrary nonzero monodromy parameter. The result is established for a WKB expansion of two different Lax pairs associated with the Painlevé 2 system, namely the Jimbo-Miwa Lax pair and the Harnad-Tracy-Widom Lax pair, where a small parameter $$\hbar $$ is introduced by a proper rescaling. The proof is based on showing that these systems satisfy the topological type property introduced in Bergère et al. (Ann Henri Poincaré 16:2713, 2015), Bergère and Eynard (, 2009). In the process, we explain why the insertion operator method traditionally used to prove the topological type property is currently incomplete and we propose new methods to bypass the issue. Our work generalizes similar results obtained from random matrix theory in the special case of vanishing monodromies (Borot and Eynard in , 2010; , 2010). Explicit computations up to $$g=3$$ are provided along the paper as an illustration of the results. Eventually, taking the time parameter t to infinity we observe that the symplectic invariants $$F^{(g)}$$ of the Jimbo-Miwa and Harnad-Tracy-Widom spectral curves converge to the Euler characteristic of moduli space of genus g Riemann surfaces. [ABSTRACT FROM AUTHOR]

We continue the previously started study of the development of a direct method for constructing the Lax pair for a given integrable equation. This approach does not require any addition assumptions about the properties of the equation. As one equation of the Lax pair, we take the linearization of the considered nonlinear equation, and the second equation of the pair is related to its generalized invariant manifold. The problem of seeking the second equation reduces to simple but rather cumbersome calculations and, as examples show, is effectively solvable. It is remarkable that the second equation of this pair allows easily finding a recursion operator describing the hierarchy of higher symmetries of the equation. At first glance, the Lax pairs thus obtained differ from usual ones in having a higher order or a higher matrix dimensionality. We show with examples that they reduce to the usual pairs by reducing their order. As an example, we consider an integrable double discrete system of exponential type and its higher symmetry for which we give the Lax pair and construct the conservation laws. [ABSTRACT FROM AUTHOR]

Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with an arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients. [ABSTRACT FROM AUTHOR]

Agents endowed with power compete for a divisible resource by forming coalitions with other agents. The coalition with the greatest power wins the resource and divides it among its members. The agents' power increases according to their share of the resource.We study two models of coalition formation where winning agents accumulate power and losing agents may participate in further coalition formation processes. An axiomatic approach is provided by focusing on variations of two main axioms: self-enforcement, which requires that no further deviation happens after a coalition has formed, and rationality, which requires that agents pick the coalition that gives them their highest payoff. For these alternative models, we determine the existence of stable coalitions that are self-enforcing and rational for two traditional sharing rules. The models presented in this paper illustrate how power accumulation, the sharing rule, and whether losing agents participate in future coalition formation processes, shape the way coalitions will be stable throughout time. [ABSTRACT FROM AUTHOR]

For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason-Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary terms appearing in the polar coordinate expression of the invariant integral. [ABSTRACT FROM AUTHOR]

In this paper, we will present a Kalman filtering algorithm that achieves better noise reduction in a single-channel speech enhancement application. The proposed method aims to tune the Kalman filter gain in order to offset the bias that is inherent when estimating speech parameters from noise-corrupted speech. After analysing the Kalman recursion equations and the filter gain, the sensitivity metric was shown to be useful in tuning the Kalman filter to achieve better noise reduction. Speech enhancement experiments were performed on the commonly available NOIZEUS database corrupted with white Gaussian noise, and the proposed method was evaluated and compared with recent speech enhancement methods, such as the STSA estimator with wavelet thresholding on multi-tapered spectra (or STSA-WT) and generalised subspace method. The proposed method was shown to produce better quality speech than the STSA-WT estimator, while being competitive with the generalised subspace method. Spectrogram analysis demonstrated that the proposed method could achieve similar levels of noise reduction to the Kalman filter in the oracle case. [ABSTRACT FROM AUTHOR]

We investigate the soft behaviour of scalar effective field theories (EFTs) when there is a number of distinct derivative power counting parameters, ρ < ρ < . . . < ρ . We clarify the notion of an enhanced soft limit and use these to extend the scope of on-shell recursion techniques for scalar EFTs. As an example, we perform a detailed study of theories with two power counting parameters, ρ = 1 and ρ = 2, that include the shift symmetric generalised galileons. We demonstrate that the minimally enhanced soft limit uniquely picks out the Dirac-Born-Infeld (DBI) symmetry, including DBI galileons. For the exceptional soft limit we uniquely pick out the special galileon within the class of theories under investigation. We study the DBI galileon amplitudes more closely, verifying the validity of the recursion techniques in generating the six point amplitude, and explicitly demonstrating the invariance of all amplitudes under DBI galileon duality. [ABSTRACT FROM AUTHOR]

We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov-Witten invariants can be derived. [ABSTRACT FROM AUTHOR]

We consider four mixed problems for the string vibration equation with zero initial conditions, with a Bitsadze-Samarskii boundary condition of the general form at the right endpoint, and with an inhomogeneous Neumann or Dirichlet condition at the left endpoint. We prove the uniqueness of a generalized solution (in the sense of Il'in) of these problems and obtain an analytic representation of these solutions. The solution of each of the problems is represented in the form of a linear combination of functions constructed from the problem data, and recursion formulas for the coefficients of this linear combination are obtained. [ABSTRACT FROM AUTHOR]

In Ramsey's Theorem and Recursion Theory, Theorem 4.2, Jockusch proved that for any computable k-coloring of pairs of integers, there is an infinite $$\Pi ^0_2$$ homogeneous set. The proof used a countable collection of $$\Pi ^0_2$$ sets as potential infinite homogeneous sets. In a remark preceding the proof, Jockusch stated without proof that it can be shown that there is no computable way to prove this result with a finite number of $$\Pi ^0_2$$ sets. We provide a proof of this claim, showing that there is no computable way to take an index for an arbitrary computable coloring and produce a finite number of indices of $$\Pi ^0_2$$ sets with the property that one of those sets will be homogeneous for that coloring. While proving this result, we introduce n-trains as objects with useful combinatorial properties which can be used as approximations to infinite $$\Pi ^0_2$$ sets. [ABSTRACT FROM AUTHOR]

There are several ways to understand computability over first-order structures. We may admit functions given by arbitrary recursive definitions, or we may restrict ourselves to 'iterative,' or tail recursive, functions computable by nothing more complicated than while loops. It is well known that in the classical case of recursion theory over the natural numbers, these two notions of computability coincide (though this is not true for all structures). We ask if there are structures over which recursion and tail recursion coincide in terms of computability, but in which a general recursive program may compute a certain function more efficiently than any tail recursion, according to some natural measure of complexity. We give a positive answer to this question, thus answering an open question in Lynch and Blum (Math. Syst. Theory. 12(1), 205-211 [5]). [ABSTRACT FROM AUTHOR]

In this note, we study the Q-cut representation by combining it with BCFW deformation. As a consequence, the one-loop integrand is expressed in terms of a recursion relation, i.e., n-point one-loop integrand is constructed using tree-level amplitudes and m- point one-loop integrands with m ≤ n - 1. By giving explicit examples, we show that the integrand from the recursion relation is equivalent to that from Feynman diagrams or the original Q-cut construction, up to scale free terms. [ABSTRACT FROM AUTHOR]

We describe a new method to explore recursive cognition in the visual domain. We define recursion as the ability to represent multiple hierarchical levels using the same rule, entailing the ability to generate new levels beyond those previously encountered. With this definition recursion can be distinguished from general hierarchical embedding. To investigate this recursion/hierarchy distinction in the visual domain, we developed two novel methods: The Visual Recursion Task (VRT), in which an inferred rule is used to represent new hierarchical levels, and the Embedded Iteration Task (EIT), in which additional elements are added to an existing hierarchical level. We found that adult humans can represent recursion in the visuo-spatial domain, and that this ability is distinct from both general intelligence and the ability to represent iterative processes embedded within hierarchical structures. Compared with embedded iteration, visual recursion correlated positively with other recursive planning tasks (Tower of Hanoi), but not with specific visuo-spatial resources (spatial short-term memory and working memory). We conclude that humans are able to use recursive representations to process complex visuo-spatial hierarchies and that our visual recursion task taps into specific cognitive resources. This method opens exciting opportunities to explore the relationship between visual recursion and language. [ABSTRACT FROM AUTHOR]

The fastest known algorithms for computing the R* consensus tree of k rooted phylogenetic trees with n leaves each and identical leaf label sets run in $$O(n^{2} \sqrt{\log n})$$ time when $$k = 2$$ (Jansson and Sung in Algorithmica 66(2):329-345, 2013) and $$O(k n^{3})$$ time when $$k \ge 3$$ (Bryant in Bioconsensus, volume 61 of DIMACS series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp 163-184, 2003). This paper shows how to compute it in $$O(n^{2})$$ time for $$k = 2, O(n^{2} \log ^{4/3} n)$$ time for $$k = 3$$ , and $$O(n^{2} \log ^{k+2} n)$$ time for unbounded k. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the analysis of the queue length and waiting time distributions in a batch arrival $$M^X/G/1$$ retrial queue. Necessary and sufficient conditions are obtained for the existence of the moments of the queue length and waiting time distributions. We also provide recursive formulas for the higher order moments of the queue length and waiting time distributions. [ABSTRACT FROM AUTHOR]

The foundation scheme in set theory asserts that every nonempty class has an $$\in $$ -minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and $$\alpha $$ -recursion theory. We take KP set theory without foundation (called KP $$^-$$ ) as the base theory. We show that KP $$^-$$ + $$\Pi _1$$ -Foundation + $$V=L$$ is enough to carry out finite injury arguments in $$\alpha $$ -recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. [ABSTRACT FROM AUTHOR]

We introduce the concept of a generic relation for algorithmic problems, which preserves the property of being decidable for a problem for almost all inputs and possesses the transitive property. As distinct from the classical m-reducibility relation, the generic relation under consideration does not possess the reflexive property: we construct an example of a recursively enumerable set that is generically incomparable with itself. We also give an example of a set that is complete with respect to the generic relation in the class of recursively enumerable sets. [ABSTRACT FROM AUTHOR]

We present a framework for statically detecting deadlocks in a concurrent object-oriented language with asynchronous method calls and cooperative scheduling of method activations. Since this language features recursion and dynamic resource creation, deadlock detection is extremely complex and state-of-the-art solutions either give imprecise answers or do not scale. In order to augment precision and scalability, we propose a modular framework that allows several techniques to be combined. The basic component of the framework is a front-end inference algorithm that extracts abstract behavioral descriptions of methods, called contracts, which retain resource dependency information. This component is integrated with a number of possible different back-ends that analyze contracts and derive deadlock information. As a proof-of-concept, we discuss two such back-ends: (1) an evaluator that computes a fixpoint semantics and (2) an evaluator using abstract model checking. [ABSTRACT FROM AUTHOR]