An evolutionary approach to anomalous intuition

Intuition has always been associated with a hint of the anomalous, with credible examples of intuitive knowledge that appear to arise from the future or from distant locations without sensory mediation. Experimental and anecdotal evidence exists to suggest that a complete understanding of intuition will need to include these anomalous aspects of intuition. To that end it is important to recognize that an understanding of anomalous intuition, though presenting considerable challenges to physics and neuroscience, may not require ‘paranormal’ explanations or entities outside the compass of science. Anomalous intuition has traditionally been studied within the field of parapsychology where is it known as extrasensory perception (ESP). One model of ESP proposes two stages. In the first stage, the process, the anomalous information is ‘received’ and in the second stage, the product, the anomalous information is elaborated into conscious awareness and/or behaviour. The process is a challenge primarily for physics, and physicists both within parapsychology and in the mainstream are addressing it. The product, anomalous intuition, is grounded in normal psychological activity and is a problem for psychology and neuroscience to understand. In order to understand how ESP or anomalous intuition works, it is necessary to understand its purpose within an evolutionary context. Evolution has proven exceptionally effective in enabling species to make use of a wide range of physical phenomena for information gathering and communication. If some yet undiscovered physical process permits retrocausation would we not expect evolution to have capitalized on that process. As a product of evolution, ESP would have to conform to the requirements of evolutionary theory. Suddendorf and Corballis (2007) have elaborated the notion of mental time travel (MTT), the memory-based ability to project oneself into the past as well as the future, and have argued that the “ultimate evolutionary advantage” may lie in the capacity to envisage future events. Their model of MTT provides an ideal context in which to understand an evolutionary path for anomalous intuition. Working through the emotional system, anomalous intuition may operate by influencing the selection of memory images we use to execute our MTT. A growing body of data supports the involvement of the emotional system in anomalous intuition but there is only suggestive evidence for the expected hereditary component. The observed limited effectiveness of anomalous intuition may emerge from the balance achieved through an evolutionarily stable strategy, or result from inherent limitations in capitalizing on the underlying physical proces

For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances

The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost function is the parameter dependent objective function of the QAOA. We demonstrate that if the parameters are fixed and the instance comes from a reasonable distribution then the objective function value is concentrated in the sense that typical instances have (nearly) the same value of the objective function. This applies not just for optimal parameters as the whole landscape is instance independent. We can prove this is true for low depth quantum circuits for instances of MaxCut on large 3-regular graphs. Our results generalize beyond this example. We support the arguments with numerical examples that show remarkable concentration. For higher depth circuits the numerics also show concentration and we argue for this using the Law of Large Numbers. We also observe by simulation that if we find parameters which result in good performance at say 10 bits these same parameters result in good performance at say 24 bits. These findings suggest ways to run the QAOA that reduce or eliminate the use of the outer loop optimization and may allow us to find good solutions with fewer calls to the quantum computer.Comment: 16 pages, 1 figur

On the multiplicity of the hyperelliptic integrals

Let $I(t)= \oint_{\delta(t)} \omega$ be an Abelian integral, where $H=y^2-x^{n+1}+P(x)$ is a hyperelliptic polynomial of Morse type, $\delta(t)$ a horizontal family of cycles in the curves $\{H=t\}$, and $\omega$ a polynomial 1-form in the variables $x$ and $y$. We provide an upper bound on the multiplicity of $I(t)$, away from the critical values of $H$. Namely: $ord\ I(t) \leq n-1+\frac{n(n-1)}{2}$if$\deg \omega <\deg H=n+1$. The reasoning goes as follows: we consider the analytic curve parameterized by the integrals along$\delta(t)$of the$n$``Petrov'' forms of$H$(polynomial 1-forms that freely generate the module of relative cohomology of$H$), and interpret the multiplicity of$I(t)$as the order of contact of$\gamma(t)$and a linear hyperplane of$\textbf C^ n$. Using the Picard-Fuchs system satisfied by$\gamma(t)$, we establish an algebraic identity involving the wronskian determinant of the integrals of the original form$\omega$along a basis of the homology of the generic fiber of$H$. The latter wronskian is analyzed through this identity, which yields the estimate on the multiplicity of$I(t)$. Still, in some cases, related to the geometry at infinity of the curves$\{H=t\} \subseteq \textbf C^2$, the wronskian occurs to be zero identically. In this alternative we show how to adapt the argument to a system of smaller rank, and get a nontrivial wronskian. For a form$\omega$of arbitrary degree, we are led to estimating the order of contact between$\gamma(t)$and a suitable algebraic hypersurface in$\textbf C^{n+1}$. We observe that$ord I(t)$grows like an affine function with respect to$\deg \omega$.Comment: 18 page

Beans ( Phaseolus spp.) - model food legumes

Globally, 800 million people are malnourished. Heavily subsidised farmers in rich countries produce sufficient surplus food to feed the hungry, but not at a price the poor can afford. Even donating the rich world's surplus to the poor would not solve the problem. Most poor people earn their living from agriculture, so a deluge of free food would destroy their livelihoods. Thus, the only answer to world hunger is to safeguard and improve the productivity of farmers in poor countries. Diets of subsistence level farmers in Africa and Latin America often contain sufficient carbohydrates (through cassava, corn/maize, rice, wheat, etc.), but are poor in proteins. Dietary proteins can take the form of scarce animal products (eggs, milk, meat, etc.), but are usually derived from legumes (plants of the bean and pea family). Legumes are vital in agriculture as they form associations with bacteria that 'sfix-nitrogen' from the air. Effectively this amounts to internal fertilisation and is the main reason that legumes are richer in proteins than all other plants. Thousands of legume species exist but more common beans (Phaseolus vulgaris L.) are eaten than any other. In some countries such as Mexico and Brazil, beans are the primary source of protein in human diets. As half the grain legumes consumed worldwide are common beans, they represent the species of choice for the study of grain legume nutrition. Unfortunately, the yields of common beans are low even by the standards of legumes, and the quality of their seed proteins is sub-optimal. Most probably this results from millennia of selection for stable rather than high yield, and as such, is a problem that can be redressed by modern genetic techniques. We have formed an international consortium called Phaseomics' to establish the necessary framework of knowledge and materials that will result in disease-resistant, stress-tolerant, high-quality protein and high-yielding beans. Phaseomics will be instrumental in improving living conditions in deprived regions of Africa and the Americas. It will contribute to social equity and sustainable development and enhance inter- and intra-cultural understanding, knowledge and relationships. A major goal of Phaseomics is to generate new common bean varieties that are not only suitable for but also desired by the local farmer and consumer communities. Therefore, the socio-economic dimension of improved bean production and the analysis of factors influencing the acceptance of novel varieties will be an integral part of the proposed research (see Figure 1). Here, we give an overview of the economic and nutritional importance of common beans as a food crop. Priorities and targets of current breeding programmes are outlined, along with ongoing efforts in genomics. Recommendations for an international coordinated effort to join knowledge, facilities and expertise in a variety of scientific undertakings that will contribute to the overall goal of better beans are given. To be rapid and effective, plant breeding programmes (i.e., those that involve crossing two different 'sparents') rely heavily on molecular 'smarkers'. These genetic landmarks are used to positio

Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry

We consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y^2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces.Comment: v2: slightly expanded expositio

An Empirical Charge Transfer Potential with Correct Dissociation Limits

The empirical valence bond (EVB) method [J. Chem. Phys. 52, 1262 (1970)] has always embodied charge transfer processes. The mechanism of that behavior is examined here and recast for use as a new empirical potential energy surface for large-scale simulations. A two-state model is explored. The main features of the model are: (1) Explicit decomposition of the total system electron density is invoked; (2) The charge is defined through the density decomposition into constituent contributions; (3) The charge transfer behavior is controlled through the resonance energy matrix elements which cannot be ignored; and (4) A reference-state approach, similar in spirit to the EVB method, is used to define the resonance state energy contributions in terms of "knowable" quantities. With equal validity, the new potential energy can be expressed as a nonthermal ensemble average with a nonlinear but analytical charge dependence in the occupation number. Dissociation to neutral species for a gas-phase process is preserved. A variant of constrained search density functional theory is advocated as the preferred way to define an energy for a given charge.Comment: Submitted to J. Chem. Phys. 11/12/03. 14 pages, 8 figure