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Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations Open
We consider all degenerate scalar-tensor theories that depend quadratically\non second order derivatives of a scalar field, which we have identified in a\nprevious work. These theories, whose degeneracy in general ensures the absence\nof O…
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Uniqueness of Einstein Kähler Metrics Modulo Connected Group Actions Open
Throughout this paper, we fix an arbitrary n-dimensional compact complex manifold X with positive first Chern class cl(Xh>O.We then put f: the set of all Kahler forms on X representing 27!'c1(X)R' f+: ={w E f I w has positive definite Ricc…
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Bootstrapping a Five-Loop Amplitude Using Steinmann Relations Open
The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the …
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Homotopy characterization of non-Hermitian Hamiltonians Open
We revisit the problem of classifying topological band structures in\nnon-Hermitian systems. Recently, a solution has been proposed, which is based\non redefining the notion of energy band gap in two different ways, leading to\nthe so-call…
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Secure State Estimation Against Sensor Attacks in the Presence of Noise Open
We consider the problem of estimating the state of a noisy linear dynamical\nsystem when an unknown subset of sensors is arbitrarily corrupted by an\nadversary. We propose a secure state estimation algorithm, and derive (optimal)\nbounds o…
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On Unlimited Sampling and Reconstruction Open
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the f…
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QUASI-SYMMETRIC FUNCTIONS AND MOD <b><i>p </i></b>MULTIPLE HARMONIC SUMS Open
We present a number of results about (finite) multiple harmonic sums modulo a\nprime, which provide interesting parallels to known results about multiple zeta\nvalues (i.e., infinite multiple harmonic series). In particular, we prove a\n"d…
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Program synthesis using conflict-driven learning Open
We propose a new conflict-driven program synthesis technique that is capable of learning from past mistakes. Given a spurious program that violates the desired specification, our synthesis algorithm identifies the root cause of the conflic…
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1-form symmetries of 4d N=2 class S theories Open
We determine the 1-form symmetry group for any 4d $\\mathcal{N}$ = 2 class S theory constructed by compactifying a 6d $\\mathcal{N}$ =(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has…
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Optimization Modulo Theories with Linear Rational Costs Open
In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade, efficient SMT solvers have been developed for seve…
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Image Encryption Based on Fourier-DNA Coding for Hyperchaotic Chen System, Chen-Based Binary Quantization S-Box, and Variable-Base Modulo Operation Open
This research work extends the hyperchaotic 4D Chen system into the fractional-order domain to carry out image encryption over 3 stages. For the first encryption stage, the discrete Fourier transform (DFT) of the numerical solution of the …
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cvc4sy: Smart and Fast Term Enumeration for Syntax-Guided Synthesis Open
We present cvc4sy, a syntax-guided synthesis (SyGuS) solver based on three bounded term enumeration strategies. The first encodes term enumeration as an extension of the quantifier-free theory of algebraic datatypes. The second is based on…
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A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial Open
We establish a new family of q -supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q -microscoping and the Chinese remainder theorem for polynomials.
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A Modulo-Based Architecture for Analog-to-Digital Conversion Open
Systems that capture and process analog signals must first acquire them through an analog-to-digital converter. While subsequent digital processing can remove statistical correlations present in the acquired data, the dynamic range of the …
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Adjacency matrices of zero-divisor graphs of integers modulo<i>n</i> Open
We study adjacency matrices of zero-divisor graphs of [math] for various [math] . We find their determinant and rank for all [math] , develop a method for finding nonzero eigenvalues, and use it to find all eigenvalues for the case [math] …
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Unifying Search-based and Compilation-based Approaches to Multi-agent Path Finding through Satisfiability Modulo Theories Open
We unify search-based and compilation-based approaches to multi-agent path finding (MAPF) through satisfiability modulo theories (SMT). The task in MAPF is to navigate agents in an undirected graph to given goal vertices so that they do no…
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Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions Open
Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some theory or combination of theories; Verification Modulo Theories (VMT) is the problem of analyzing the reachabi…
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Non-weight modules over the Heisenberg–Virasoro algebra and the W algebra W(2,2) Open
In this paper, we construct and study some non-weight modules for the Heisenberg–Virasoro algebra and the [Formula: see text] algebra [Formula: see text]. We determine the modules, whose restriction to the universal enveloping algebra of t…
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When to Finish? Optimal Beam Search for Neural Text Generation (modulo beam size) Open
In neural text generation such as neural machine translation, summarization, and image captioning, beam search is widely used to improve the output text quality. However, in the neural generation setting, hypotheses can finish in different…
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Depth-graded motivic multiple zeta values Open
We study the depth filtration on multiple zeta values, on the motivic Galois group of mixed Tate motives over $\mathbb {Z}$ and on the Grothendieck–Teichmüller group, and its relation to modular forms. Using period polynomials for cusp for…
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On the Planning Abilities of Large Language Models : A Critical Investigation Open
Intrigued by the claims of emergent reasoning capabilities in LLMs trained on general web corpora, in this paper, we set out to investigate their planning capabilities. We aim to evaluate (1) the effectiveness of LLMs in generating plans a…
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Hybrid Quantum Protocols for Secure Multiparty Summation and Multiplication Open
The summation and multiplication are two basic operations for secure multiparty quantum computation. The existing secure multiparty quantum summation and multiplication protocols have ( n , n ) threshold approach and their computation type…
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SMC: Satisfiability Modulo Convex Programming Open
The design of cyber-physical systems (CPSs) requires methods and tools that can efficiently reason about the interaction between discrete models, e.g., representing the behaviors of 'cyber' components, and continuous models of physical pro…
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On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n Open
Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex s…
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Linear temporal logic motion planning for teams of underactuated robots using satisfiability modulo convex programming Open
We present an efficient algorithm for multi-robot motion planning from linear temporal logic (LTL) specifications. We assume that the dynamics of each robot can be described by a discrete-time, linear system together with constraints on th…
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Parameters of LCD BCH codes with two lengths Open
In this paper, we study LCD BCH codes over the finite field GF$(q)$ with two types of lengths $n$, where $n = q^l+1$ and $n = (q^l+1)/(q+1)$. Several classes of LCD BCH codes are given and their parameters are determined or bounded by expl…
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Taking a vector supermultiplet apart: Alternative Fayet–Iliopoulos-type terms Open
Starting from an Abelian ${\\cal N}=1$ vector supermultiplet $V$ coupled to\nconformal supergravity, we construct from it a nilpotent real scalar Goldstino\nsuperfield $\\mathfrak V$ of the type proposed in arXiv:1702.02423. It contains\no…
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The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments Open
The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF allows for high-dynamic-range (HDR) signal reconstruction by conve…
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Strong Subconvexity for Self-Dual GL(3) <i>L</i>-Functions Open
In this paper, we prove strong subconvexity bounds for self-dual $\textrm {GL}(3)\ L$-functions in the $t$-aspect and for $\textrm {GL}(3)\times \textrm {GL}(2)$$L$-functions in the $\textrm {GL}(2)$-spectral aspect. The bounds are strong …
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SMT-based verification of parameterized systems Open
It is well known that verification of safety properties of sequential programs is reducible to satisfiability modulo theory of a first-order logic formula, called a verification condition (VC). The reduction is used both in deductive and a…