Tootfinder

An elementary derivation of 3-cycles for a quadratic map
Arpad Benyi, Ioan Casu
https://arxiv.org/abs/2510.12558 https://arxiv.org/pdf/2510.12558

An elementary derivation of 3-cycles for a quadratic map
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergen…

Spiral Model Technique For Data Science & Machine Learning Lifecycle
Rohith Mahadevan
https://arxiv.org/abs/2510.06987 https://arxiv.org/pdf/2510.06987…

Spiral Model Technique For Data Science & Machine Learning Lifecycle
Analytics play an important role in modern business. Companies adapt data science lifecycles to their culture to seek productivity and improve their competitiveness among others. Data science lifecycles are fairly an important contributing factor to start and end a project that are data dependent. Data science and Machine learning life cycles comprises of series of steps that are involved in a project. A typical life cycle states that it is a linear or cyclical model that revolves around. It is…

Two Proofs of the Hamiltonian Cycle Identity
Hamilton Sawczuk, Edinah Gnang
https://arxiv.org/abs/2510.02473 https://arxiv.org/pdf/2510.02473

Two Proofs of the Hamiltonian Cycle Identity
The Hamiltonian cycle polynomial can be evaluated to count the number of Hamiltonian cycles in a graph. It can also be viewed as a list of all spanning cycles of length $n$. We adopt the latter perspective and present a pair of original proofs for the Hamiltonian cycle identity which relates the Hamiltonian cycle polynomial to the important determinant and permanent polynomials. The first proof is a more accessible combinatorial argument. The second proof relies on viewing polynomials as both l…

Dynamical Systems Models for Market Evolution: A Mechanistic Alternative to Autoregressive Methods
Aparna Komarla, Max Hill
https://arxiv.org/abs/2510.06778 https://

Dynamical Systems Models for Market Evolution: A Mechanistic Alternative to Autoregressive Methods
We present a novel approach to modeling market dynamics using ordinary differential equations that explicitly incorporates product competitiveness and consumer behavior. Our framework treats market segments as interacting populations in a dynamical system analogous to predator-prey models, where competitive advantages drive market share transitions through mechanistic modeling of market flows including new product adoption, refresh cycles, and obsolescence dynamics.

Classification of Thouless pumps with non-invertible symmetries and implications for Floquet phases
Yabo Li, Matteo Dell'acqua, Aditi Mitra
https://arxiv.org/abs/2510.01626 …

Classification of Thouless pumps with non-invertible symmetries and implications for Floquet phases
We study symmetry preserving adiabatic and Floquet dynamics of one-dimensional systems. Using quasiadiabatic evolution, we establish a correspondence between adiabatic cycles and invertible defects generated by spatially truncated Thouless pump operators. Employing the classification of gapped phases by module categories, we show that the Thouless pumps are classified by the group of autoequivalences of the module category. We then explicitly construct Thouless pump operators for minimal lattic…

Cyclic Variational Quantum Eigensolver: Escaping Barren Plateaus through Staircase Descent
Hao Zhang, Ayush Asthana
https://arxiv.org/abs/2509.13096 https://

Cyclic Variational Quantum Eigensolver: Escaping Barren Plateaus through Staircase Descent
We introduce the Cyclic Variational Quantum Eigensolver (CVQE), a hardware-efficient framework for accurate ground-state quantum simulation on noisy intermediate-scale quantum (NISQ) devices. CVQE departs from conventional VQE by incorporating a measurement-driven feedback cycle: Slater determinants with significant sampling probability are iteratively added to the reference superposition, while a fixed entangler (e.g., single-layer UCCSD) is reused throughout. This adaptive reference growth sy…

A Chinese restaurant process for multiset permutations
Dudley Stark
https://arxiv.org/abs/2509.13979 https://arxiv.org/pdf/2509.13979

A Chinese restaurant process for multiset permutations
Multisets are like sets, except that they can contain multiple copies of their elements. If there are $n_i$ copies of $i$, $1\leq i\leq t$, in multiset $M_t$, then there are $\binom{n_1+\cdots+n_t}{n_1,\ldots, n_t}$ possible permutations of $M_t$. Knuth showed how to factor any multiset permutation into cycles. For fixed $n_i$, $i\geq 1$, we show how to adapt the Chinese restaurant process, which generates random permutations on $n$ elements with weighting $θ^{\# \, {\rm cycles}}$, $θ>0$, seq…