On the neglected role of hominin body-pocket use as means of addressing transport problems

Body-pockets are areas afforded by bodies that can be used to hold and/or transport objects to solve transport problems. Several lines of evidence – from animals (such as apes) to modern humans – point toward the likely use of body-pockets by all hominins. Here we highlight the neglect in the literature of accounting for hominin body-pocket usage. We argue that it is likely that body-pockets were used – at least sometimes – by hominins, and that, specifically, bipedal hominin body-pocket usage would have included the use of armpit-pockets. Hominins would have, at least sometimes, held and/or transported objects such as artefacts, including stone artefacts. This is the body-pocket / armpit-pocket hypothesis. Additionally, and independently of the body-pocket hypothesis more generally, we speculate that body-pocket usage could have influenced also aspects of the forms of carried objects – indirectly (via selecting) and/or directly (via forming). Three mutually exclusive theoretical possibilities remain. Possibility 1 (i.e. the current status quo): Any hominin body-pocket influence on objects’ forms was absent – or never sufficiently large to have left any recognisable pattern today. Possibility 2: There was a hominin body-pocket influence on objects’ forms, and this influence – while perhaps small – was large enough, at least sometimes and/or in some cases, to be recognisable today. Possibility 3 (the body-pocket fitting hypothesis): There was a hominin body-pocket influence on objects’ forms, and this influence was so large that it best explains large or complete parts of these forms completely. In our manuscript we tentatively reject Possibility 3. As for the remaining possibilities, Possibility 1 currently proved more parsimonious than Possibility 2. While we present data that is consistent with Possibility 2, no strong evidence was found to support it – rendering it a speculative and weak hypothesis. We outline possible future examinations of the body-pocket fitting hypothesis, but we conclude that the current status quo (i.e. Possibility 1) regarding the sources of hominin artefact forms remains unchanged.

Extender-based forcings with overlapping extenders and negations of the Shelah Weak Hypothesis

Extender-based Prikry–Magidor forcing for overlapping extenders is introduced. As an application, models with strong forms of negations of the Shelah Weak Hypothesis for various cofinalities are constructed.

Extreme Multiclass Classification Criteria

We analyze the theoretical properties of the recently proposed objective function for efficient online construction and training of multiclass classification trees in the settings where the label space is very large. We show the important properties of this objective and provide a complete proof that maximizing it simultaneously encourages balanced trees and improves the purity of the class distributions at subsequent levels in the tree. We further explore its connection to the three well-known entropy-based decision tree criteria, i.e., Shannon entropy, Gini-entropy and its modified variant, for which efficient optimization strategies are largely unknown in the extreme multiclass setting. We show theoretically that this objective can be viewed as a surrogate function for all of these entropy criteria and that maximizing it indirectly optimizes them as well. We derive boosting guarantees and obtain a closed-form expression for the number of iterations needed to reduce the considered entropy criteria below an arbitrary threshold. The obtained theorem relies on a weak hypothesis assumption that directly depends on the considered objective function. Finally, we prove that optimizing the objective directly reduces the multi-class classification error of the decision tree.

On the typical size and cancellations among the coefficients of some modular forms

We obtain a nontrivial upper bound for almost all elements of the sequences of real numbers which are multiplicative and at the prime indices are distributed according to the Sato–Tate density. Examples of such sequences come from coefficients of severalL-functions of elliptic curves and modular forms. In particular, we show that |τ(n)| ⩽n11/2(logn)−1/2+o(1)for a set ofnof asymptotic density 1, where τ(n) is the Ramanujan τ function while the standard argument yields log 2 instead of −1/2 in the power of the logarithm. Another consequence of our result is that in the number of representations ofnby a binary quadratic form one has slightly more than square-root cancellations for almost all integersn.In addition, we obtain a central limit theorem for such sequences, assuming a weak hypothesis on the rate of convergence to the Sato–Tate law. For Fourier coefficients of primitive holomorphic cusp forms such a hypothesis is known conditionally and might be within reach unconditionally using the currently established potential automorphy.

Quantum AdaBoost algorithm via cluster state

The principle and theory of quantum computation are investigated by researchers for many years, and further applied to improve the efficiency of classical machine learning algorithms. Based on physical mechanism, a quantum version of AdaBoost (Adaptive Boosting) training algorithm is proposed in this paper, of which purpose is to construct a strong classifier. In the proposed scheme with cluster state in quantum mechanism is to realize the weak learning algorithm, and then update the corresponding weight of examples. As a result, a final classifier can be obtained by combining efficiently weak hypothesis based on measuring cluster state to reweight the distribution of examples.

Multiobjective Stopping Problem for Discrete-Time Markov Processes: Convex Analytic Approach

The purpose of this paper is to study an optimal stopping problem with constraints for a Markov chain with general state space by using the convex analytic approach. The costs are assumed to be nonnegative. Our model is not assumed to be transient or absorbing and the stopping time does not necessarily have a finite expectation. As a consequence, the occupation measure is not necessarily finite, which poses some difficulties in the analysis of the associated linear program. Under a very weak hypothesis, it is shown that the linear problem admits an optimal solution, guaranteeing the existence of an optimal stopping strategy for the optimal stopping problem with constraints.

Multiobjective Stopping Problem for Discrete-Time Markov Processes: Convex Analytic Approach

The purpose of this paper is to study an optimal stopping problem with constraints for a Markov chain with general state space by using the convex analytic approach. The costs are assumed to be nonnegative. Our model is not assumed to be transient or absorbing and the stopping time does not necessarily have a finite expectation. As a consequence, the occupation measure is not necessarily finite, which poses some difficulties in the analysis of the associated linear program. Under a very weak hypothesis, it is shown that the linear problem admits an optimal solution, guaranteeing the existence of an optimal stopping strategy for the optimal stopping problem with constraints.