optimization

Learn how Siemens Simcenter’s AI-powered simulation tools achieved 15% mass reduction and 166x faster crash predictions—demonstrated through a Star Wars AT-ST walker optimization case study.

Mathematics readiness at entry remains critical for success in first-year engineering programs, yet many institutions lack transparent, reusable tools to diagnose risk and design levelling policies. This study develops and evaluates an open Engineering Mathematics Readiness Score (EMRS) using two publicly available datasets: the UCI Student Performance dataset in secondary-school mathematics and …

The capability of one architecture to simulate another serves as the foundation for network comparison, with embedding playing a key role in analyzing these simulations. In architectural simulation, graph embedding is one of the most powerful techniques for executing parallel algorithms and modeling diverse interconnection networks. In our earlier work, we listed an open problem that the determin…

I wrote this code to split a number into equations which gives the least cost. e.g. 6896 = (64 + 19) ** 2 + 7 which has a cost of 1.909 points which is the most optimized equation with least cost. The ...

This paper investigates the mathematical and philosophical necessity of "Unity" (1) as a dynamic equilibrium between the Bounded Past (0) and the Unbounded Future (Infinity). Moving beyond traditional ontological definitions, the work demonstrates that disparate systems—from quantum mechanics to cognitive identity—share a common structural requirement for a stable normalization floor. I argue tha…

- Ponder This Given a square binary matrix of order , such that the sum of each row and column of is 1, we can find the lowest such that , the identity matrix. Denote by the maximum such when going over all the matrices in satisfying the above condition. For example, and . Your goal: Find . A bonus "*" will be given for finding . Related posts - PuzzleGadi Aleksandrowicz - PuzzleGadi Aleksandrowi…

Active search for bifurcations Psarellis, Yorgos M; Sapsis, Themistoklis P; Kevrekidis, Ioannis G Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden (“hard”) transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding of observed dynamic behavior, but also for designing efficient…

Naively multiplying two $2 \times 2$ matri- ces requires eight multiplications and four additions. Strassen showed how to perform the same computation using seven multiplications and 18 additions. By chang- ing basis, Karstadt and Schwartz lowered the number of additions to 12, which they showed to be optimal within this generalized Karstadt-Schwartz (KS) framework. We present improved methods f…

Are there examples of plurisubharmonic functions that are bounded below but not continuous?

Her research aims to advance the state-of-the-art contextual stochastic optimization methodologies, providing tools for making smarter decisions when the future is uncertain. The post USC Viterbi’s Karmel S. Shehadeh Lands Prestigious AFOSR Grant appeared first on USC Viterbi | School of Engineering .

IntroductionRadio labeling of graphs extends the channel assignment problem by assigning non-negative integers to vertices of a connected graph G such that |h(℘)−h(𝓆)|≥diam(ℊ)+1−d(℘, 𝓆). The objective is to minimize the span, leading to the radio number rn(G).MethodsWe consider a class of outerplanar graphs with vertex set {u1, v1, x1, …, xn, y1, …, yn} and a structured edge set combining path an…

Understanding how wounds heal after injury could be a step closer thanks to a new mathematical model developed by researchers at the University of Bristol.

This paper extends Load Minimization Theory (LMT) to addiction recovery by modeling pathological attachment as a high-load fixation in a damped pendulum system with strong attachment parameter k(t). Numerical simulations over 200 time units compared CBT-only, Standard Pharma+CBT, and Early Pharma+CBT conditions. Results demonstrated cumulative load reductions of approximately 28%, 38%, and 42%, r…

Abstract This paper defines a minimal condition for the persistence of constraint-governed systems under scale. A system remains structurally admissible only while entropy introduced by generation is matched or exceeded by constraint-induced entropy reduction or admissible redistribution of probability mass. Formally: \Delta H_{gen}(t) \le \Delta C_{stab}(t) Where: * H: entropy over the admissibl…

Let $\gamma:[0,1]\to\mathbb{R}^N$ be a rectifiable curve and $\ell(\gamma)$ be its length. Also denote $\Gamma=\{\gamma(t)|\ t\in [0,1]\}$ the image of $\gamma$. Is it true that for each ...

Optimal (Euclidean) Metric Compression Indyk, Piotr; Wagner, Tal We study the problem of representing all distances between 𝑛 points in ℝ𝑑, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for ℓ1 (also known as Manhattan)-metrics, and for general metrics. Our bounds for Euclidean metrics mark the first i…

The routing algorithms, constraint satisfaction problems, and distributed coordination behind moving 10,000+ vehicles per day Introduction When you request a quote to ship your car from New York to Los Angeles, you see a simple price and a pickup window. What you don't see is the complex optimization problem that just got created behind the scenes. Auto transport is a fascinating case study in lo…

The BCa bootstrap interval can be understood not merely as a higher-order endpoint correction, but as a small piece of frequentist inferential geometry. We isolate a rigorous core for that interpretation. A simple exponential-tilt object built directly from jackknife data recovers the familiar BCa bias and curvature corrections exactly. The classical BCa adjustment is then shown to arise as the u…

Scientific Reports, Published online: 23 April 2026; doi:10.1038/s41598-026-48948-8 An optimization method for railway alignment schemes based on game-theoretic combination weighting and an interval number model

Load Minimization Theory (LMT) proposes that the total relational load L(R) = U(R) + F(R) + E(R) is the universal principle governing all dynamics. Building upon the previous short paper, this extended paper develops three key advances: (1) a geometric formulation of the relational operator R(t) as a point on a relational manifold equipped with an information-geometric metric g_R; (2) a general t…