20 papers · ranked by Valyu relevance
Bryant, Dustin, Jim Woodcock, Simon J. Foster
This paper presents a formalized analysis of the sigmoid function and a fully mechanized proof of the Universal Approximation Theorem (UAT) in Isabelle/HOL, a higher-order logic theorem prover. The sigmoid function plays a fundamental role in neural networks; yet, its formal properties, such as differentiability…
Changin Oh, Kathleen P. Wilkie
We present the Toroidal Search Algorithm (TSA), a novel population-based metaheuristic optimization method inspired by the topology of a torus. Conventional metaheuristics frequently suffer from boundary stagnation, a phenomenon that severely degrades performance in bounded and high-dimensional search spaces. TSA…
Chintan Panchal, Ankur Changela, Mohendra Roy
Efficient hardware implementation of nonlinear activation functions is a crucial task in deploying artificial neural networks on resource-constrained and edge devices such as Field-Programmable Gate Arrays (FPGAs). The sigmoid activation function is widely used for probabilistic output, binary classification, and…
Fatoumata Mangane, Ruben Casanova, Kyra JE Borgman, Leanne De Koning + 7 more
Multiplexed imaging technologies now enable the simultaneous profiling of hundreds to thousands of molecular targets in intact tissues, providing unprecedented insight into cellular heterogeneity and spatial organization. While data generation has rapidly matured, the quantitative analysis of spatial structure remains…
Jhon Manuel Portella Delgado, Ankit Goel
This paper presents a constraint-lifting control framework for designing stabilizing controllers that guarantee the forward invariance of a prescribed safe set. State-of-the-art safety-enforcing methods, such as control barrier functions (CBFs) and model predictive control (MPC), typically rely on solving constrained…
Changsoo Shin
Modern AI systems excel at pattern recognition and task execution, but they often fall short of replicating the layered, self-referential structure of human thought that unfolds over time. In this paper, we present a mathematically grounded and conceptually simple framework based on smoothed step functions-sigmoid…
Castaldo, Francesca, Aristides, Raul de Palma + 6 more
Brain dynamics dominate every level of neural organization—from single-neuron spiking to the macroscopic waves captured by fMRI, MEG, and EEG—yet the mathematical tools used to interrogate those dynamics remain scattered across a patchwork of traditions. Neural mass models (NMMs) (aggregate neural models) provide one…
Tuan Minh Pham, Thinh V. Cao, Việt Cường Nguyễn, Huy Phương Nguyễn + 2 more
The sigmoid gate in mixture-of-experts (MoE) models has been empirically shown to outperform the softmax gate across several tasks, ranging from approximating feed-forward networks to language modeling. Additionally, recent efforts have demonstrated that the sigmoid gate is provably more sample-efficient than its…
Micha Hacohen, Miriam Gundellman, Ilan Dinstein
The transition from wake to stable sleep is characterized by multiple neural, physiological, and behavioral changes. How these changes may differ in individuals with difficulties falling asleep such as children with neurodevelopmental conditions is poorly understood. Here, we studied sleep initiation in >2000 nights…
S. Vidhusha, S. Karthika, N. Sahana, A. Sabari Srinivas + 3 more
Learning disabilities in children are exhibited through difficulties in reading and writing due to lack of cognitive skills. It is generally diagnosed by analyzing the behavior and processing capacity of children by understanding their academic candidature. This can also be evidenced by capturing and analyzing their…
Siyao Huang, Yong Deng, Małgorzata Przybyła-Kasperek
Conflict management is crucial in information fusion. One of the efficient algorithms to address conflicting data fusion is discounting method. However, how to determine the discounting coefficient in conflict management remains an open issue. A heuristic method to determine discounting coefficient is presented based…
Batoul Saab, Jihad Fahs, Arij Daou
Conductance-based models of neuronal excitability depend critically on the mathematical form used to describe voltage-dependent ion channel gating. The classical Hodgkin-Huxley (HH) formalism employs empirically derived rate expressions fitted to squid giant axon data that are not readily transferable across cell types…
Authors not listed
A growth curve is S-shaped and typically contains three phases, namely, the lag phase, the exponential phase, and the saturation phase. Similarly, the time-series data of atmospheric CO2 levels over the past thousand years trend like the lag phase of growth until around 1940 and enter an exponential phase like curve…
Dai-Nghia Vy, Van-Thuan Nguyen, Quyet-Thang Huynh, Trung-Nghia Phung + 2 more
Context: Many models based on S-shaped functions demonstrate their advantages in non-homogeneous Poisson process software reliability modeling. However, three well-known types have been used without deep mathematical evaluation. Furthermore, some other promising S-shaped functions should be aimed at. Objectives: (1)…
Authors not listed
We report a new charge model and a new general small molecule force field. Here, we address the development and benchmarking of both the Open Force Field (OpenFF) AshGC charge model, as well as the Sage 2.3.0 small molecule force field for drug-like molecules. AshGC is a graph neural network-based method for efficient…
Mahmut Sabri Medişoğlu, Melisa Öçbe
Purpose The sigmoid sinus is a vital dural venous structure whose anatomical variability has direct implications for lateral skull base and otologic surgeries. Understanding the sinus’s positional variations is considered important for minimizing surgical risks. This study aimed to evaluate the morphological…
Jingmeng Cui, Dieta Wagenmakers, G. Sander van Doorn, Fred Hasselman + 1 more
Formal theories translate verbal theories into a mathematical representation, such as a coupled differential equation or other dynamical systems, intending to strengthen the deductive power of (clinical) theories and to formulate testable and novel hypotheses. Work in clinical formal theories mainly relies on…
Mika Ohkawa, Ying Joey Zhou, Saskia Haegens, Matin Jafarian
Learning new information in the presence of distracters and changing conditions requires the ability to adapt. In the brain, this adaptive capability has been linked to dynamic interactions between attention and working memory, which enable the selective filtering of irrelevant input while preserving behaviorally…
Authors not listed
Nonlinear monotonically increasing bounded functions help to visualize and analyze data on various scales. However, many monotonic functions such as logarithm or power laws have either function values or derivatives that become unbounded at some regions of the $x-$ axis. On the other hand, sigmoid or hyperbolic…
Mikal Daou, Tihana Jovanic, Alain Destexhe
Building a simple model that precisely and functionally characterizes a neuron is a challenging and important task to select the best concise and computationally efficient model. However, this type of work has only been done for subthreshold properties of neurons. Here, we take a different perspective and suggest a…