Related papers: On variables with few occurrences in conjunctive n…
We consider constraint satisfaction problems parameterized above or below tight bounds. One example is MaxSat parameterized above $m/2$: given a CNF formula $F$ with $m$ clauses, decide whether there is a truth assignment that satisfies at…
An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms \[ \begin{cases} F = c_{1}x_1^3 + c_{2}x_2^3 + \cdots + c_{n}x_n^3 = 0, \\ G = d_{1}x_1^3 + d_{2}x_2^3 + \cdots + d_{n}x_n^3 =…
The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
The minimal excludant statistic, which denotes the smallest positive integer that is not a part of an integer partition, has received great interest in recent years. In this paper, we move on to the smallest positive integer whose frequency…
Modern generative and vision-language models (VLMs) are increasingly used in scientific and medical decision support, where predicted probabilities must be both accurate and well calibrated. Despite strong empirical results with moderate…
We consider the large deviations associated with the empirical mean of independent and identically distributed random variables under a subexponential moment condition. We show that non-trivial deviations are observable at a subexponential…
It is a classical fact that every $n$-element set of positive reals has at least $\binom{n+1}{2}+1$ distinct subset sums, with equality exactly for homogeneous arithmetic progressions (when $n\geq 4$). We establish stability versions of…
The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric…
It is known that there are classes of 2-CNFs requiring exponential size non-deterministic read-once branching programs to compute them. However, to the best of our knowledge, there are no superpolynomial lower bounds for branching programs…
We show the existence and multiplicity of concentrating solutions to a pure Neumann slightly supercritical problem in a ball. This is the first existence result for this kind of problems in the supercritical regime. Since the solutions must…
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state…
We study the lower tail behavior of the least singular value of an $n\times n$ random matrix $M_n := M+N_n$, where $M$ is a fixed complex matrix with operator norm at most $\exp(n^{c})$ and $N_n$ is a random matrix, each of whose entries is…
This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-McCullough Positivstellensatz, the noncommutative analog of…
We study the following natural variation on the classical universality problem: given a language $L(M)$ represented by $M$ (e.g., a DFA/RE/NFA/PDA), does there exist an integer $\ell \geq 0$ such that $\Sigma^\ell \subseteq L(M)$? In the…
The XOR-satisfiability (XORSAT) problem requires finding an assignment of $n$ Boolean variables that satisfy $m$ exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances,…
We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with…
Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…
We let $\mathcal{F}$ be a finite family of sets closed under taking unions and $\emptyset \not \in \mathcal{F}$, and call an element abundant if it belongs to more than half of the sets of $\mathcal{F}$. In this notation, the classical…
A nearly linear recurrence sequence (nlrs) is a complex sequence $(a_n)$ with the property that there exist complex numbers $A_0$,$\ldots$, $A_{d-1}$ such that the sequence $\big(a_{n+d}+A_{d-1}a_{n+d-1}+\cdots +A_0a_n\big)_{n=0}^{\infty}$…