Minimising biases in Full Configuration Interaction Quantum Monte Carlo

We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov Chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to in general minimise the bias. We show a reweighting scheme to remove the bias caused by population control commonly used in Diffusion Monte Carlo [J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step.Comment: Supplementary material available as 'Ancillary Files

Superposition as memory: unlocking quantum automatic complexity

Imagine a lock with two states, "locked" and "unlocked", which may be manipulated using two operations, called 0 and 1. Moreover, the only way to (with certainty) unlock using four operations is to do them in the sequence 0011, i.e., $0^n1^n$ where $n=2$. In this scenario one might think that the lock needs to be in certain further states after each operation, so that there is some memory of what has been done so far. Here we show that this memory can be entirely encoded in superpositions of the two basic states "locked" and "unlocked", where, as dictated by quantum mechanics, the operations are given by unitary matrices. Moreover, we show using the Jordan--Schur lemma that a similar lock is not possible for $n=60$. We define the semi-classical quantum automatic complexity $Q_{s}(x)$ of a word $x$ as the infimum in lexicographic order of those pairs of nonnegative integers $(n,q)$ such that there is a subgroup $G$ of the projective unitary group PU$(n)$ with $|G|\le q$ and with $U_0,U_1\in G$ such that, in terms of a standard basis $\{e_k\}$ and with $U_z=\prod_k U_{z(k)}$, we have $U_x e_1=e_2$ and $U_y e_1 \ne e_2$ for all $y\ne x$ with $|y|=|x|$. We show that $Q_s$ is unbounded and not constant for strings of a given length. In particular, $$Q_{s}(0^21^2)\le (2,12) < (3,1) \le Q_{s}(0^{60}1^{60})$$ and $Q_s(0^{120})\le (2,121)$.Comment: Lecture Notes in Computer Science, UCNC (Unconventional Computation and Natural Computation) 201

Review: Neuropathology findings in autonomic brain regions in SUDEP and future research directions

Autonomic dysfunction is implicated from clinical, neuroimaging and experimental studies in sudden and unexpected death in epilepsy (SUDEP). Neuropathological analysis in SUDEP series enable exploration of acquired, seizure-related cellular adaptations in autonomic and brainstem autonomic centres of relevance to dysfunction in the peri-ictal period. Alterations in SUDEP compared to control groups have been identified in the ventrolateral medulla, amygdala, hippocampus and central autonomic regions. These involve neuropeptidergic, serotonergic and adenosine systems, as well as specific regional astroglial and microglial populations, as potential neuronal modulators, orchestrating autonomic dysfunction. Future research studies need to extend to clinically and genetically characterized epilepsies, to explore if common or distinct pathways of autonomic dysfunction mediate SUDEP. The ultimate objective of SUDEP research is the identification of disease biomarkers for at risk patients, to improve post-mortem recognition and disease categorisation, but ultimately, for exposing potential treatment targets of pharmacologically modifiable and reversible cellular alterations

Polyglucosan bodies in medullary catecholaminergic neurones in SUDEP

Polyglucosan bodies have been reported in the context of hypoxic-ischaemic perinatal brain injury, mainly in the pallidum but with rare reports in brainstem neurones. We report a case of a five year old boy with cerebral palsy, complex neurology and epilepsy with a sudden nocturnal death. At post-mortem long-standing bilateral necrosis of basal ganglia and hippocampal atrophy was identified in keeping with hypoxic-ischaemic perinatal injury. In addition numerous polyglucosan bodies, which were PAS, p62 and ubiquitin positive, were noted in brainstem neurones and dendrites, primarily involving the ventrolateral and dorsomedial medulla. Immunohistochemistry confirmed relative preservation of medullary neuronal populations in the reticular formation, including catecholaminergic (tyrosine hydroxylase, TH), serotonergic (tryptophan hydroxylase) and neurokinin1 receptor/somatostatin positive neurones. The polyglucosan bodies predominated in catecholaminergic neurones which could indicate their selective vulnerability and a functional deficiency, which during a critical peri-ictal period contributed to the sudden death in epilepsy

Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project

The HANDE quantum Monte Carlo project offers accessible stochastic algorithms for general use for scientists in the field of quantum chemistry. HANDE is an ambitious and general high-performance code developed by a geographically-dispersed team with a variety of backgrounds in computational science. In the course of preparing a public, open-source release, we have taken this opportunity to step back and look at what we have done and what we hope to do in the future. We pay particular attention to development processes, the approach taken to train students joining the project, and how a flat hierarchical structure aids communicationComment: 6 pages. Submission to WSSSPE

Morse homology for the heat flow

We use the heat flow on the loop space of a closed Riemannian manifold to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined in the spirit of Floer theory by counting, modulo time shift, heat flow trajectories that converge asymptotically to nondegenerate closed geodesics of Morse index difference one.Comment: 89 pages, 3 figure

Responses to supplementation by dairy cows given low pasture allowances in different seasons 2. Milk production

Two factorial experiments were designed to determine the effects of stage of lactation, and season of the year, on cow responses to supplementary feeding. These experiments were conducted over consecutive years with 128 high genetic merit multiparous Holstein-Friesian cows in early, mid and late lactation in spring, summer, autumn and winter. At each stage of lactation, and in each season of the year, cows were offered a restricted pasture allowance (25 to 35 kg dry matter (DM) per cow per day), either unsupplemented (control) or with supplement at 50 MJ metabolizable energy (ME) per cow per day in experiment 1 and 80 MJ ME per cow per day in experiment 2. The two supplements given in both years were rolled maize grain (MG) and a mixture of foods formulated to nutritionally balance the diet (BR). In experiment 2, another treatment, of a generous pasture allowance (60 to 75 kg DM per cow per day) (AP), was imposed on an additional group of early lactation cows during each season. Direct milk solids (MS) (milk fat plus milk protein) responses in experiment 1 to MG were 169, 279, 195 and 251 g MS per cow per day in spring, summer, autumn and winter, respectively, while those to BR were 107, 250, 192, 289 g MS per cow per day. In experiment 2, however, milk solids responses to both supplements during spring were slightly below the control treatment, with values similar to those in experiment 1 in summer and autumn for cows on the BR but not the MG supplement. Milk solids responses to supplementary foods were largest during seasons of the year when the quantity and quality of pasture on offer resulted in the lowest milk solids yield from unsupplemented cows. When carry-over effects of feeding MG and BR on milk solids production were detected, they were only about half the magnitude of the direct effects. Serum urea concentrations were higher in control cows than those offered MG with a similar effect for BR in all but summer in experiment 1, while serum glucose concentrations were highest in winter and lowest in summer. The most important factor influencing milk solids responses was the relative food deficit (RFD) represented by the decline in milk solids yield of the respective control groups after,changing from a generous pasture allowance to restricted allowance when the feeding treatments were imposed. Total milk solids responses (direct and carry-over) to supplements were greatest when severe food restrictions, relative to the cows' current food demand, resulted in large reductions in milk solids yield of the control groups. The RFD was the best predictor of milk solids response to supplementary foods. Therefore, it is likely that cows are most responsive to supplementary foods during or immediately after the imposition of a severe food restriction

Responses to supplementation by dairy cows given low pasture allowances in different seasons 1. Pasture intake and substitution

Two factorial experiments were designed to determine the effects of stage of lactation, and season of the year, on cow responses to supplementary feeding. These experiments were conducted over consecutive years with 128 high genetic merit multiparous Holstein-Friesian cows in early, mid and late lactation in spring, summer, autumn and winter. At each stage of lactation, and in each season of the year, cows were offered a restricted pasture allowance (25 to 35 kg dry matter (DM) per cow per day), either unsupplemented (control) or supplemented with 50 MJ metabolizable energy (ME) per cow per day in experiment 1 and 80 MJ ME per cow per day in experiment 2. Two different supplements were offered, namely, rolled maize grain (MG) and a mixture of foods (BR) formulated to nutritionally balance the diet. In experiment 2, a fourth treatment consisting solely of a generous pasture allowance (60 to 75 kg DM per cow per day, AP) was introduced. Offering MG and BR increased DM intake (DMI). At the restricted pasture allowance, increasing total ME allowance (MEA) by offering supplementary foods increased ME intake (MEI) by 0.68 (s.e. 0.047) MJ per extra MJ ME offered. This highly significant (P < 0.001) linear relationship was consistent across seasons, and did not diminish at higher MEA. In experiment 2, cows in early lactation had lower substitution rates than mid and late lactation cows irrespective of season. Substitution rate was higher when higher pasture allowance or quality of pasture on offer enabled the unsupplemented cows to achieve higher DMI from pasture than at other times of the year. These results suggest that one of the key factors determining the intake response to supplementary foods is pasture allowance. Within spring calving dairying systems, the largest increases in total DMI per kg of supplement offered is likely when offering supplements to early lactation cows grazing restricted allowances of high quality pasture

Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses

We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist \emph{two topologically distinct quantum phases}. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is new: one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity, and the phase of the condensate can be continuously wound and unwound