Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of M_X^{gp}-torsors on a logarithmically smooth curve $X$ over a standard logarithmic point as a logarithmic analogue of the Picard group of $X$. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on $X$ and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

South Sudan's infrastructure : a continental perspective

Newly independent South Sudan faces a challenge in making its own way in infrastructure development. Despite earning $6 billion in oil revenues since 2005, South Sudan's spending has not been proportional to its income, but rather has lagged behind North Sudan's development of infrastructure and social support. South Sudan benefitted from strong donor support during 2004-10, the interim period defined by the Comprehensive Peace Agreement. It focused on reestablishing regional transport links and access to seaports as well as rehabilitating its ports, airstrips, and single rail line. South Sudan also successfully liberalized the ICT sector. Nonetheless, the new country's infrastructure remains in such a dismal state that it is difficult to pinpoint a single most pressing challenge. The transport sector accounts for half of the country's spending needs, and water and sanitation account for a further quarter of the total. But so many improvements are needed that the nation cannot realistically catch up with its neighbors within 10 years, or even longer. South Sudan's annual infrastructure funding gap is$879 million per year. Given that the country's total needs are beyond its reach in the medium term, it must adopt firm priorities for its infrastructure spending. It also must attract international and private-sector investment and look to lower-cost technologies to begin to close its funding gap. Although South Sudan loses relatively little to inefficiencies, redressing those inefficiencies will be vital to creating solid institutions to attract new investors and get the most out of their investments.Transport Economics Policy&Planning,E-Business,Infrastructure Economics,Energy Production and Transportation,Roads&Highways

Sudan's infrastructure : a continental perspective

Improvements in infrastructure across Sudan in recent years have contributed 1.7 percentage points to the country's per capita growth. Consistent with trends in other countries, the ICT revolution that swept Africa contributed more than any other sector to growth in Sudan. Raising the infrastructure endowment of all parts of Sudan to that of the region's best performer -- Mauritius -- could boost annual growth by about 3.5 percentage points. Sudan has heavily invested in infrastructure in recent years. Notable achievements include tripling power-generation capacity, liberalizing the ICT sector, and connecting to an undersea fiber-optic cable. Looking ahead, Sudan's most pressing infrastructure challenges lie in the water and transport sectors. In the water sector, the country needs to dramatically improve access to safe sources of water and sanitation while improving utility efficiency. In the transport sector the country needs to vastly expand rural and international connectivity and improve quality across the network. Sudan presently spends about $1.5 billion per year on infrastructure, with$580 million a year lost to inefficiencies. Even if the inefficiencies were eliminated, however, Sudan would face an infrastructure funding gap of $2.9 billion per year. This gap could be reduced by half by choosing lower-cost water, sanitation, and road-surfacing technologies, and could be bridged by continuing to capture financing from the private sector and abroad.Transport Economics Policy&Planning,Infrastructure Economics,Energy Production and Transportation,E-Business,Banks&Banking Reform

Accountability

A week into the anti-racism protests that followed the chilling murder of George Floyd by a Minnesota police officer, the co-founder of Black Lives Matter (BLM), Patrisse Cullors, appeared on ABC’s Nightline. The show recapped the extraordinary events of that day: US President Donald Trump had announced that he was ‘dispatching thousands and thousands of heavily armed soldiers, military personnel, and law enforcement officers’ to quell the demonstrations. Federal police and military troops had used tear gas, rubber bullets and flash grenades on peaceful protestors gathered around the White House to clear the route to a cynical photo-op: the President posing before a church that he did not enter, holding aloft a Bible that he did not open

Thermo-Chemical Modelling of the Production of Ferro-chromium in Submerged-Arc Furnace

Several studies have been reported in literature on the thermochemistry of production of ferro-chromium. Experimental studies have been carried out to understand the kinetics of reduction of oxides and to study the equilibrium between slag and metal in the furnace. How-ever, a quantitative model of the thermochemistry of the process in any region of the furnace is yet to be repor-ted. Pre-reduction of the ore has been recommended and also employed as a means of reducing the power consumption in the furnace is yet to explored. This communication reports a thermochemical model for the production of ferro-chromium in submerged-arc furnace and a model to map the temperature profile in the furnace. The neffect of pre-reduction on the temperature profile has also been asse-ssed

Experimental Processing of some of the Indian Clays for Chemical Purposes

Clays are of various types viz.,fire clays ball clays, stoneware clays, pipe clays, brick clays, bento-nite, kaolin etc. Excepting the last, the rest are avai-lable in sufficient purity and no dressing is usually necessary. Kaolin is to be washed free of gritty material in suitably designed washers

Learning Redundant Motor Tasks With and Without Overlapping Dimensions: Facilitation and Interference Effects

Prior learning of a motor skill creates motor memories that can facilitate or interfere with learning of new, but related, motor skills. One hypothesis of motor learning posits that for a sensorimotor task with redundant degrees of freedom, the nervous system learns the geometric structure of the task and improves performance by selectively operating within that task space. We tested this hypothesis by examining if transfer of learning between two tasks depends on shared dimensionality between their respective task spaces. Human participants wore a data glove and learned to manipulate a computer cursor by moving their fingers. Separate groups of participants learned two tasks: a prior task that was unique to each group and a criterion task that was common to all groups. We manipulated the mapping between finger motions and cursor positions in the prior task to define task spaces that either shared or did not share the task space dimensions (x-y axes) of the criterion task. We found that if the prior task shared task dimensions with the criterion task, there was an initial facilitation in criterion task performance. However, if the prior task did not share task dimensions with the criterion task, there was prolonged interference in learning the criterion task due to participants finding inefficient task solutions. These results show that the nervous system learns the task space through practice, and that the degree of shared task space dimensionality influences the extent to which prior experience transfers to subsequent learning of related motor skills

Congestion-aware wireless network-on-chip for high-speed communication

The design of system-on-chip (SoC) requires the complex integration between a multi-number of cores on a single chip. To establish the effective communication between multiple cores there aremore challenging issues on designing the network-on-chip (NoC) architectures. The proposed system deals with the utilization of on-chip antennas for the wireless communication between the long distance cores to minimize the latency and power. In this proposed work, we have designed high-speed wireless NoC (WiNoC) for on-chip communication. This high-speed WiNoC has been achieved by designing a congestion measure unit, which monitors and measures the congestion in the input data and establishes the effective wireless communication between the output channels and routers. The designed architecture is synthesized and implemented by using Altera Quartus II, where the SoC is designed using Qsys builder. The proposed WiNoC shows better performance parameters like throughput, latency and power than the conventional NoC

Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of MgpX -torsors on a logarithmically smooth curve X over a standard logarithmic point as a logarithmic analogue of the Picard group of X. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on X and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

Coarse-graining intramolecular hydrodynamic interaction in dilute solutions of flexible polymers

We present a scheme for coarse-graining hydrodynamic interactions in an isolated flexible homopolymer molecule in solution. In contrast to the conventional bead-spring model that employs spherical beads of fixed radii to represent the hydrodynamic characteristics of coarse-grained segments, we show that our procedure leads naturally to a discrete model of a polymer molecule as a chain of orientable and stretchable Gaussian blobs. This model accounts for both intrablob and interblob hydrodynamic interactions, which depend on the instantaneous shapes of the blobs. In Brownian dynamics simulations of initially stretched chains relaxing under quiescent conditions, the transient evolution of the mean-square end-to-end distance and first normal stress difference obtained with the Gaussian-blob model are found to be less sensitive to the degree of coarse graining, in comparison with the conventional bead-spring model with Rotne-Prager-Yamakawa hydrodynamic interactions