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Winnipeg-based Conquest Planning, which uses AI to help financial advisors and other clients make decisions, raised an $80M Series B led by Goldman Sachs (Jon Fingas/BetaKit)
https://betakit.com/conquest-planning-

Conquest Planning raises $110-million Series B to fuel US expansion of its financial management platform | BetaKit
Growth Equity at Goldman Sachs Alternatives led the Winnipeg startup’s latest funding round.

Degenerate Sheffer-type polynomials and degenerate Sheffer polynomials associated with a random variable
Taekyun Kim, Dae san Kim
https://arxiv.org/abs/2507.20167 https://

Degenerate Sheffer-type polynomials and degenerate Sheffer polynomials associated with a random variable
This paper has two primary contributions. First, we explore degenerate Sheffer-type polynomials, a hybrid of higher-order degenerate Bernoulli and Euler polynomials, and derive their properties. Second, assuming that the moment generating function of Y exists in a neighborhood of the origin, we introduce the degenerate Sheffer polynomials associated with Y. We then investigate their properties in general and for the specific cases of uniform and Bernoulli random variables. We also present new r…

Linear operators preserving volume polynomials
Lukas Grund, June Huh, Mateusz Micha{\l}ek, Hendrik S\"uss, Botong Wang
https://arxiv.org/abs/2506.22415

Linear operators preserving volume polynomials
Volume polynomials measure the growth of Minkowski sums of convex bodies and of tensor powers of positive line bundles on projective varieties. We show that Aluffi's covolume polynomials are precisely the polynomial differential operators that preserve volume polynomials, reflecting a duality between homology and cohomology. We then present several applications to matroid theory.

Model Predictive Adversarial Imitation Learning for Planning from Observation
Tyler Han, Yanda Bao, Bhaumik Mehta, Gabriel Guo, Anubhav Vishwakarma, Emily Kang, Sanghun Jung, Rosario Scalise, Jason Zhou, Bryan Xu, Byron Boots
https://arxiv.org/abs/2507.21533

Model Predictive Adversarial Imitation Learning for Planning from Observation
Human demonstration data is often ambiguous and incomplete, motivating imitation learning approaches that also exhibit reliable planning behavior. A common paradigm to perform planning-from-demonstration involves learning a reward function via Inverse Reinforcement Learning (IRL) then deploying this reward via Model Predictive Control (MPC). Towards unifying these methods, we derive a replacement of the policy in IRL with a planning-based agent. With connections to Adversarial Imitation Learnin…

Algebraic aspects of the polynomial Littlewood-Offord problem
Zhihan Jin, Matthew Kwan, Lisa Sauermann, Yiting Wang
https://arxiv.org/abs/2505.23335 https:…

Algebraic aspects of the polynomial Littlewood-Offord problem
Consider a degree-$d$ polynomial $f(ξ_1,\dots,ξ_n)$ of independent Rademacher random variables $ξ_1,\dots,ξ_n$. To what extent can $f(ξ_1,\dots,ξ_n)$ concentrate on a single point? This is the so-called polynomial Littlewood-Offord problem. A nearly optimal bound was proved by Meka, Nguyen and Vu: the point probabilities are always at most about $1/\sqrt n$, unless $f$ is "close to the zero polynomial" (having only $o(n^d)$ nonzero coefficients). In this paper we prove several results s…

A polynomial approach to Carlitz's $q$-Bernoulli numbers
Mohamed Mouzaia, Bakir Farhi
https://arxiv.org/abs/2507.20384 https://arxiv.org/pdf/2507.20384…

A polynomial approach to Carlitz's $q$-Bernoulli numbers
This paper investigates $q$-analogues of the classical Bernoulli polynomials and numbers. We introduce a new polynomial sequence ${\left(B_{n , q}(X)\right)}_{n \in \mathbb{N}_0}$, defined via the Jackson integral, and explore its connections with Carlitz's $q$-Bernoulli polynomials and numbers. Specifically, we prove that the numbers $B_{n , q}(0)$ are exactly the Carlitz $q$-Bernoulli numbers and that the polynomials $B_{n , q}(X)$ are genuine $q$-analogues of the classical Bernoulli polynomi…

RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric
Yu Zhang, Xiao-Song Yang
https://arxiv.org/abs/2506.22170 https://…

RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric
The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or all other nodes based on non-negative edge weights. Numerous studies have focused on the Dijkstra algorithm due to its potential application. However, its application in surface path planning for mobile robots remains largely unexplored. In this letter, a surface optimal path planning algorithm called RM-Dijkstra is p…

This https://arxiv.org/abs/2208.14711 has been replaced.
link: https://scholar.google.com/scholar?q=a

On real roots of polynomial systems of equations in the context of group theory
The probability that a zero of a random real polynomial of increasing degree is real tends to zero. However, passing from polynomials to Laurent polynomials yields a surprising result: the probability that a root is real tends not to zero, but to $1/\sqrt{3}$. A similar phenomenon has also been observed for systems of Laurent polynomials in several variables. By considering Laurent polynomials as functions associated with torus representations, we describe an analogous phenomenon for representa…

A MILP-Based Solution to Multi-Agent Motion Planning and Collision Avoidance in Constrained Environments
Akshay Jaitly, Jack Cline, Siavash Farzan
https://arxiv.org/abs/2506.21982

A MILP-Based Solution to Multi-Agent Motion Planning and Collision Avoidance in Constrained Environments
We propose a mixed-integer linear program (MILP) for multi-agent motion planning that embeds Polytopic Action-based Motion Planning (PAAMP) into a sequence-then-solve pipeline. Region sequences confine each agent to adjacent convex polytopes, while a big-M hyperplane model enforces inter-agent separation. Collision constraints are applied only to agents sharing or neighboring a region, which reduces binary variables exponentially compared with naive formulations. An L1 path-length-plus-accelera…

Pretraining a Unified PDDL Domain from Real-World Demonstrations for Generalizable Robot Task Planning
Haoming Ye, Yunxiao Xiao, Cewu Lu, Panpan Cai
https://arxiv.org/abs/2507.21545

Pretraining a Unified PDDL Domain from Real-World Demonstrations for Generalizable Robot Task Planning
Robotic task planning in real-world environments requires reasoning over implicit constraints from language and vision. While LLMs and VLMs offer strong priors, they struggle with long-horizon structure and symbolic grounding. Existing methods that combine LLMs with symbolic planning often rely on handcrafted or narrow domains, limiting generalization. We propose UniDomain, a framework that pre-trains a PDDL domain from robot manipulation demonstrations and applies it for online robotic task pl…