Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

Who is sowing our seeds? A systematic review of the use of plant genetic resources in research

Collections of plant genetic resources managed by genebanks function to conserve the range of genetic diversity present in crop genepools. They can facilitate access to valuable allelic variation for both plant breeders and researchers who are able to request germplasm for use in crop improvement and both basic and applied scientific research. The direct impact of genebank collections is often unclear as downstream uses of germplasm samples may not be reported back to the genebank of origin. This study aims to systematically review scientific use of germplasm using the UK Vegetable Genebank (UKVGB) as a model. Between the years of 1980–2016, a total of 271 publications were identified as using UKVGB material. The frequency of publications and the international nature of use increased significantly over the time period studied. Accessions directly sourced from the UKVGB made up the majority of material used by researchers, but material from research-derived resources such as differential sets and core collections or diversity sets have also been used. Resistance to pests and diseases and genetic diversity were the main topics of study although germplasm was used to address a wide range of other research questions. Genebanks such as UKVGB provide an essential resource of allelic diversity in crop genepools which supports a diverse range of research projects. The utilisation of these plant genetic resources has increased over time, contributing to a substantial number of publications. Developments in sequencing technologies have no doubt played a part as larger numbers of accessions can be utilized in a single experiment, but the increase also no doubt reflects a greater interest in the use of allelic diversity to overcome challenges in crop improvement and research

The sand and gravel resources of the country around Shotley and Felixstowe, Suffolk : description of 1:25,000 resource sheet TM 23

It has become increasingly clear in recent years that an assessment of resources of many minerals should be undertaken. This is a Report of the Mineral Assessment Unit which was set up in May 1968 to undertake such work. It describes and quantifies the resources of sand and gravel of 44.3 krn2 of country around Shotley and Felixstowe, Suffolk, shown on the accompanying 1:25 000 resource sheet TM 23. This survey is concerned with assessing sand and gravel resources on a regional scale at the indicated level; the deposits are not outlined completely nor their grade established throughout. The work may be regarded as the application to large areas of methods used commercially for evaluating reserves on small sites. It may be regarded also as an extension of geological mapping by providing information about the thickness and quality of deposits. The survey was conducted during 1968 to 1970 by Dr R. Allender, assisted by Mr S. E. Hollyer as field officer, who supervised the drilling and sampling programme and helped in the preparation of data for this publication. Mr S. J. Booth also supervised drilling during the later parts of the programme. The work is based on a 1 :63 360 scale geological survey originally published in 1882 on Old Series Sheet 48 NE. The lines were transferred partly to New Series Sheet 207 (published with minor amendments in 1927) and partly to New Series Sheets 208 and 225, (published in 1928 and reprinted as a combined sheet in 1956). The geology of the area of sheet TM 23 is now presented at the 1:25 000 scale, incorporating minor amendments resulting from the present work. Mr J. W. Gardner, C. B. E. (Land Agent) has been responsible for negotiating access to land for drilling. The ready cooperation of land owners and tenants in this work is gratefully acknowledged. Special thanks are due to Dr T. L. Thomas of the Royal School of Mines for his advice on methods of resource calculation. Financial support for the survey was provided by the Department of the Environment

The sand and gravel resources of the area south and west of Woodbridge, Suffolk : description of 1:25,000 resource sheet TM 24

It has become increasingly clear in recent years that an assessment of resources of many minerals should be undertaken. This is a Report of the Mineral Assessment Unit which was set up in May 1968 to undertake such work. It describes and quantifies the resources of sand and gravel of 91.2 km2 of country south and west of Woodbridge, shown on the accompanying 1:25 000 resource sheet TM 24. This survey is concerned with assessing sand and gravel resources on a regional scale at the indicated level; the deposits are not outlined completely nor their grade establjshed throughout. The work may be regarded as the application to large areas of methods used commercially for evaluating reserves on small sites. It may be regarded also as an extension of geological mapping by providing information about the thickness and quality of deposits. The survey was conducted in 1968-69 by Dr. R. Allender assisted by Mr. S. E. Hollyer as field officer, who supervised the drilling and sampling programme and helped in the preparation of data for this publication. Mr. J. D. Ambrose supervised drilling for a short period at the beginning of the programme. The work is based on a 1:63 360 scale geological survey originally published in 1881-1883 on parts of Old Series sheets 48, 49 and 50, reprinted with corrections and additions on New Series one-inch sheets 207 (Ipswich) and 208 and 225 (Woodbridge and Felixstowe) first published in 1927 and 1928 respectively (and subsequently at intervals) and now presented at the 1:25 000 scale, incorporating minor amendments resulting from the present work. Mr. J.W. Gardner, C. B. E. (Land Agent) has been responsible for negotiating access to land for drilling. The ready cooperation of land owners and tenants in this work is gratefully acknowledged. Special thanks are due to Dr. T. L. Thomas of the Royal School of Mines, London, for his advice on methods of resource calculation. Financial support for the survey was provided by the Department of the Environment

UV luminescence characterisation of organics in Mars-analogue substrates

This project was supported by a Leverhulme Trust Research Project Grant (RPG-2015-071). C Cousins also wishes to acknowledge funding by the Royal Society of Edinburgh.Detection of organic matter is one of the core objectives of future Mars exploration. The ability to probe rocks, soils, and other geological substrates for organic targets is a high priority for in situ investigation, sample caching, and sample return. UV luminescence – the emission of visible light following UV irradiation – is a tool that is beginning to be harnessed for planetary exploration. We conducted  UV photoluminescence analyses of (i) Mars analogue sediments doped with polyaromatic hydrocarbons (PAHs; <15 ppm), (ii) carbonaceous CM chondrites and terrestrial kerogen (Type IV), and (iii) synthetic salt crystals doped with PAHs (2 ppm). We show that that detection of PAHs is possible within synthetic and natural gypsum, and synthetic halite. These substrates show the most apparent spectral modifications, suggesting that the most transparent minerals are more conducive to UV photoluminescence detection of trapped organic matter. Iron oxide, ubiquitously present on Mars surface, hampers but does not completely quench the UV luminescence emission. Finally, the maturity of organic carbonaceous material influences the luminescence response, resulting in a reduced signal for UV excitation wavelengths down to 225 nm. This study demonstrates the utility of UV luminescence spectroscopy for the analysis of mixed organic-inorganic materials applicable to Mars exploration.PostprintPeer reviewe

The accuracy of breast volume measurement methods: a systematic review

Breast volume is a key metric in breast surgery and there are a number of different methods which measure it. However, a lack of knowledge regarding a method’s accuracy and comparability has made it difficult to establish a clinical standard. We have performed a systematic review of the literature to examine the various techniques for measurement of breast volume and to assess their accuracy and usefulness in clinical practice. Each of the fifteen studies we identified had more than ten live participants and assessed volume measurement accuracy using a gold-standard based on the volume, or mass, of a mastectomy specimen. Many of the studies from this review report large (> 200 ml) uncertainty in breast volume and many fail to assess measurement accuracy using appropriate statistical tools. Of the methods assessed, MRI scanning consistently demonstrated the highest accuracy with three studies reporting errors lower than 10% for small (250 ml), medium (500 ml) and large (1,000 ml) breasts. However, as a high-cost, non-routine assessment other methods may be more appropriate

Strong Enhancement of Superconducting Correlation in a Two-Component Fermion Gas

We study high-density electron-hole (e-h) systems with the electron density slightly larger than the hole density. We find a new superconducting phase, in which the excess electrons form Cooper pairs moving in an e-h BCS phase. The coexistence of the e-h and e-e orders is possible because e and h have opposite charges, whereas analogous phases are impossible in the case of two fermion species that have the same charge or are neutral. Most strikingly, the e-h order enhances the superconducting e-h order parameter by more than one order of magnitude as compared with that given by the BCS formula, for the same value of the effective e-e attractive potential \lambda^{ee}. This new phase should be observable in an e-h system created by photoexcitation in doped semiconductors at low temperatures.Comment: 5 pages including 5 PostScript figure

PROGRESS IN REDUCING THE NUCLEAR THREAT: UNITED STATES PLUTONIUM CONSOLIDATION AND DISPOSITION

Following the end of the Cold War, the United States identified 61.5 metric tons (MT) of plutonium and larger quantities of enriched uranium that are permanently excess to use in nuclear weapons programs. The Department of Energy (DOE) also began shutting down, stabilizing, and removing inventories from production facilities that were no longer needed to support weapons programs and non-weapons activities. The storage of 'Category I' nuclear materials at Rocky Flats, Sandia National Laboratories, and several smaller sites has been terminated to reduce costs and safeguards risks. De-inventory continues at the Hanford site and the Lawrence Livermore National Laboratory. Consolidation of inventories works in concert with the permanent disposition of excess inventories, including several tonnes of plutonium that have already been disposed to waste repositories and the preparation for transfers to the planned Mixed Oxide (MOX) Fuel Fabrication Facility (for the bulk of the excess plutonium) and alternative disposition methods for material that cannot be used readily in the MOX fuel cycle. This report describes status of plutonium consolidation and disposition activities and their impacts on continuing operations, particularly at the Savannah River Site

Balancing Bounded Treewidth Circuits

Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a circuit of width $O(\log^{i+1} n)$ and size $n^c$, where $c = O(1)$, if $i=0$, and $c=O(\log \log n)$ otherwise. For our main construction, we prove that multiplicatively disjoint arithmetic circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in arithmetic formulas of depth $O(k^2\log n)$. From this we derive the analogous statement for syntactically multilinear arithmetic circuits, which strengthens a theorem of Mahajan and Rao. As another application, we derive that constant width arithmetic circuits of size $n^{O(1)}$ can be balanced to depth $O(\log n)$, provided certain restrictions are made on the use of iterated multiplication. Also from our main construction, we derive that Boolean bounded fan-in circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in formulas of depth $O(k^2\log n)$. This strengthens in the non-uniform setting the known inclusion that $SC^0 \subseteq NC^1$. Finally, we apply our construction to show that {\sc reachability} for directed graphs of bounded treewidth is in $LogDCFL$

The Impatient May Use Limited Optimism to Minimize Regret

Discounted-sum games provide a formal model for the study of reinforcement learning, where the agent is enticed to get rewards early since later rewards are discounted. When the agent interacts with the environment, she may regret her actions, realizing that a previous choice was suboptimal given the behavior of the environment. The main contribution of this paper is a PSPACE algorithm for computing the minimum possible regret of a given game. To this end, several results of independent interest are shown. (1) We identify a class of regret-minimizing and admissible strategies that first assume that the environment is collaborating, then assume it is adversarial---the precise timing of the switch is key here. (2) Disregarding the computational cost of numerical analysis, we provide an NP algorithm that checks that the regret entailed by a given time-switching strategy exceeds a given value. (3) We show that determining whether a strategy minimizes regret is decidable in PSPACE