Research works

How many labelers do you have? A closer look at gold-standard labels

The construction of most supervised learning datasets revolves around collecting multiple labels for each instance, then aggregating the labels to form a type of "true" label. We question the wisdom of this pipeline by developing a (stylized) theoretical model of this process and...

The District of Columbia Circuit Finds Article III Standing Based on the Risk of Future Identity Theft in In re U.S. Office of Personnel Management Data Security Breach Litigation

This Note examines the D.C. Circuit’s decision in In re U.S. Office of Personnel Management Data Security Breach Litigation and argues that an increased risk of future identity theft constitutes a sufficiently concrete injury for Article III standing in data breach cases. Analyzi...

The Unique Games Theorem: A Short Self-Contained Proof

We give a short proof of the theorem of OpenAI's preprint "The Unique Games Theorem" (23 September 2026). It is self-contained apart from three earlier theorems, which are stated as inputs: Håstad's parity gap, the Khot–Minzer–Safra Grassmann expansion theorem, and Dinur–Steurer...

Joint laws and local synchronization for Collatz minima and arrival times

Let m(n) be the least value on the ordinary Collatz orbit of n, and let τ(n) be its first-attainment time. We prove a spatial transfer theorem for the entire discrete pair (m(n), τ(n)). From uniform pair coalescence and a limiting minimum law, its empirical distribution becomes i...

Tilted 3-adic Syracuse laws: absolute continuity, dimension and the limits of L²

Let g1, g2, … be independent with P(g = k) = θ(1 − θ)k−1 for k ≥ 1, and let ρ = Σj≥1 3j−12−(g1+⋯+gj) in the 3-adic integers. The law μθ of ρ is a 3-adic self-similar measure for the infinitely many maps x ↦ 2−g(1 + 3x), each contracting by exactly 1/3; at θ = 1/2 it is Tao's Syra...

A Compressed Presentation of OpenAI's Proof of the Unique Games Theorem

We reconstruct the main argument of OpenAI's preprint "The Unique Games Theorem" (23 September 2026). Three earlier theorems are stated as inputs: Håstad's parity gap, the Khot–Minzer–Safra Grassmann expansion theorem, and Dinur–Steurer projection-game repetition. The remaining a...

Late synchronization and the geometry of Collatz families

We determine the geometry of Collatz trajectories conditioned on late synchronization. Their absolute odd-count separation converges, in the physical shortcut clock, to a Brownian meander continued to its first zero. One excursion carries asymptotically all the duration and heigh...

Gaussian but not locally Gaussian: the teeth of the Collatz stopping-time histogram

Let B be the set of positive integers whose Collatz orbit reaches 1, and τ(n) the total stopping time. On B, τ satisfies a central limit theorem, but it is not locally Gaussian: in ℓ¹, the histogram of τ on B ∩ (1, X) is a Gaussian times a periodic profile Ω(k − log₂X) of period...

Brownian motion in Collatz orbits

For a positive integer n let m(n) be the least value of its Collatz orbit and τ*(n) the first time the orbit reaches it; both are finite for every n, and nothing is assumed about the Collatz conjecture. We prove that the descent of a typical orbit to its minimum is a Brownian mot...

Exact rates in Collatz synchronization

Gao conjectured that his dyadic proportions of coalescing adjacent integers tend to one. We determine the exact deficiency: 1 − d̄k ~ β/√k, with β = √6·E[M]/√π and 1 ≤ E[M] < ∞, where M counts the excursions of the canonical adjacent-pair coupling. The balanced shortcut absorptio...

Gao's dyadic density-one coalescence conjecture

We give a short proof of the density-one assertion posed by Gao for consecutive Collatz starts, independent of the first public proof, due to Said Duran (September 2026). Let C be the ordinary map and let H(n, m) count halving branches among the first m ordinary steps. Write Gk(n...

Quantitative synchronization of Collatz trajectories

We study simultaneous trajectories of the ordinary Collatz map. A balanced coupling of the shortcut trajectories gives a uniform absorption estimate of order √((1 + log(1 + |d|))/h) for offset d and shortcut horizon h. Its realization preserves both the ordinary clock and the num...

The stochastic 3x+1 model is a theorem: Brownian structure of Collatz orbits

The stochastic models of the 3x+1 problem of Lagarias and Weiss, Borovkov and Pfeifer, Kontorovich and Sinai, and Kontorovich and Lagarias treat the logarithm of an orbit as a random walk. The title is meant in the following sense. For natural-density-typical n, the model's predi...

Trajectory Tracking of a Four Degree of Freedom Robotic Manipulator

A robotic manipulator can be utilized for multiple applications. As there are some expensive and bulky robotic manipulators with multi-functionalities are available in the market but not affordable for many people, a low-cost robotic manipulator, Dobot Magician, available in the...

Can we define climate by means of an ensemble? A tale of time scales of convergence

Abstract. We study the suitability of an initial condition ensemble to form the conceptual basis of defining climate. We point out that the most important criterion for this is the uniqueness of the probability measure on which the definition relies. We first naively propose, in...

There are different shades of green: heterogeneous environmental innovations and their effects on firm performance

While an established literature highlights the variety of firms' eco-innovation strategies, systematic evidence on the heterogeneous effects of different environmental innovations on different dimensions of firm performance is lacking. This study contributes to filling this resea...

A revision of the Nearctic species of Brachygluta Thomson, 1859 (Coleoptera: Staphylinidae: Pselaphinae)

The North American species of Brachygluta Thomson, 1859 are revised, treating a total of 29 species. Six names are placed as junior synonyms: Bryaxis perpunctata Brendel, 1890 (=B. luniger LeConte, 1849), B. labyrinthea Casey, 1894 (=B. intermedia Brendel, 1866), B. loripes Casey...

Corrosion-induced cracking behaviour of RC beams: experimental investigation, empirical modelling, and finite element analysis

This study investigates corrosion-induced cracking in reinforced concrete (RC) beams through experiments, empirical modelling, and finite element (FE) analysis. Specimens corroded using the galvanostatic (GS) and artificial chloride environment (ACE) methods were examined using X...

GTP orchestrates CTP synthase via an allosteric effector–cycling mechanism

Cytidine triphosphate (CTP), a fundamental building block of RNA, plays vital roles in diverse biological processes. CTP synthase (CTPS) is the only known enzyme for de novo synthesis of CTP. Efficient CTPS catalysis requires guanosine triphosphate (GTP) in a dose-dependent, nonc...

High Expression of Aurora Kinase A (AURKA) is Associated with Aggressive Tumor Biology and Therapeutic Response in ER+/HER2− Breast Cancer

Abstract Background Aurora kinase A ( AURKA ) is a serine/threonine kinase that regulates mitotic entry, spindle assembly, and chromosomal segregation. AURKA overexpression has been linked to multiple malignancies. The biological and clinical significance of AURKA expression with...