Complexity and efficient approximability of two dimensional periodically specified problems

The authors consider the two dimensional periodic specifications: a method to specify succinctly objects with highly regular repetitive structure. These specifications arise naturally when processing engineering designs including VLSI designs. These specifications can specify objects whose sizes are exponentially larger than the sizes of the specification themselves. Consequently solving a periodically specified problem by explicitly expanding the instance is prohibitively expensive in terms of computational resources. This leads one to investigate the complexity and efficient approximability of solving graph theoretic and combinatorial problems when instances are specified using two dimensional periodic specifications. They prove the following results: (1) several classical NP-hard optimization problems become NEXPTIME-hard, when instances are specified using two dimensional periodic specifications; (2) in contrast, several of these NEXPTIME-hard problems have polynomial time approximation algorithms with guaranteed worst case performance

Complexity of hierarchically and 1-dimensional periodically specified problems

We study the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale (3) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al. and (4) the hierarchical specifications of Lengauer et al. we obtain three general types of results. First, we prove that there is a polynomial time algorithm that given a 1-FPN- or 1-FPN(BC)specification of a graph (or a C N F formula) constructs a level-restricted L-specification of an isomorphic graph (or formula). This theorem along with the hardness results proved here provides alternative and unified proofs of many hardness results proved in the past either by Lengauer and Wagner or by Orlin. Second, we study the complexity of generalized CNF satisfiability problems of Schaefer. Assuming P {ne} PSPACE, we characterize completely the polynomial time solvability of these problems, when instances are specified as in (1), (2),(3) or (4). As applications of our first two types of results, we obtain a number of new PSPACE-hardness and polynomial time algorithms for problems specified as in (1), (2), (3) or(4). Many of our results also hold for O(log N) bandwidth bounded planar instances

Approximation algorithms for NEXTtime-hard periodically specified problems and domino problems

We study the efficient approximability of two general class of problems: (1) optimization versions of the domino problems studies in [Ha85, Ha86, vEB83, SB84] and (2) graph and satisfiability problems when specified using various kinds of periodic specifications. Both easiness and hardness results are obtained. Our efficient approximation algorithms and schemes are based on extensions of the ideas. Two of properties of our results obtained here are: (1) For the first time, efficient approximation algorithms and schemes have been developed for natural NEXPTIME-complete problems. (2) Our results are the first polynomial time approximation algorithms with good performance guarantees for `hard` problems specified using various kinds of periodic specifications considered in this paper. Our results significantly extend the results in [HW94, Wa93, MH+94]

Periodically specified satisfiability problems with applications: An alternative to domino problems

We characterize the complexities of several basic generalized CNF satisfiability problems SAT(S), when instances are specified using various kinds of 1- and 2-dimensional periodic specifications. We outline how this characterization can be used to prove a number of new hardness results for the complexity classes DSPACE(n), NSPACE(n), DEXPTIME, NEXPTIME, EXPSPACE etc. The hardness results presented significantly extend the known hardness results for periodically specified problems. Several advantages axe outlined of the use of periodically specified satisfiability problems over the use of domino problems in proving both hardness and easiness results. As one corollary, we show that a number of basic NP-hard problems become EXPSPACE hard when inputs axe represented using 1-dimensional infinite periodic wide specifications. This answers a long standing open question posed by Orlin

Radiometric Stability of the SABER Instrument

The SABER instrument on the National Aeronautics and Space Administration Thermosphere‐Ionosphere‐Mesosphere Energetics and Dynamics satellite continues to provide a long‐term record of Earth\u27s stratosphere, mesosphere, and lower thermosphere. The SABER data are being used to examine long‐term changes and trends in temperature, water vapor, and carbon dioxide. A tacit, central assumption of these analyses is that the SABER instrument radiometric calibration is not changing with time; that is, the instrument is stable. SABER stratospheric temperatures and those derived from Global Positioning System Radio Occultation measurements are compared to examine SABER\u27s stability. Global Positioning System Radio Occultation measurements are inherently stable due to the accuracy and traceability of the measured phase delay rate to the Système Internationale definition of the second. Differences in global annual mean SABER and COSMIC lower stratospheric temperatures show little significant change with time in the 11 years spanning 2007–2017. From this analysis we infer that SABER temperatures are stable to better than 0.1 to 0.2 K per decade

Free Recall Learning of Hierarchically Organised Lists by Adults with Asperger's Syndrome: Additional Evidence for Diminished Relational Processing

The Task Support Hypothesis (TSH, Bowler et al. Neuropsychologia 35:65–70 1997) states that individuals with autism spectrum disorder (ASD) show better memory when test procedures provide support for retrieval. The present study aimed to see whether this principle also applied at encoding. Twenty participants with high-functioning ASD and 20 matched comparison participants studied arrays of 112 words over four trials. Words were arranged either under hierarchically embedded category headings (e.g. Instruments—String—Plucked—Violin) or randomly. Both groups showed similar overall recall and better recall for the hierarchically organised words. However, the ASD participants made less use of information about relations between words and more use of item-specific information in their recall, confirming earlier reports of relational difficulties in this population

On the Complexity of Scheduling in Wireless Networks

We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K-hop interference models, under which no two links within a K-hop distance can successfully transmit at the same time. For a given K, we can obtain a throughput-optimal scheduling policy by solving the well-known maximum weighted matching problem. We show that for K > 1, the resulting problems are NP-Hard that cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, for geometric unit-disk graphs that can be used to describe a wide range of wireless networks, the problems admit polynomial time approximation schemes within a factor arbitrarily close to 1. In these network settings, we also show that a simple greedy algorithm can provide a 49-approximation, and the maximal matching scheduling policy, which can be easily implemented in a distributed fashion, achieves a guaranteed fraction of the capacity region for "all K." The geometric constraints are crucial to obtain these throughput guarantees. These results are encouraging as they suggest that one can develop low-complexity distributed algorithms to achieve near-optimal throughput for a wide range of wireless networksopen1

Hydrothermal dolomitization of basinal deposits controlled by a synsedimentary fault system in Triassic extensional setting, Hungary

Dolomitization of relatively thick carbonate successions occurs via an effective fluid circulation mechanism, since the replacement process requires a large amount of Mg-rich fluid interacting with the CaCO3 precursor. In the western end of the Neotethys, fault-controlled extensional basins developed during the Late Triassic spreading stage. In the Buda Hills and Danube-East blocks, distinct parts of silica and organic matter-rich slope and basinal deposits are dolomitized. Petrographic, geochemical, and fluid inclusion data distinguished two dolomite types: (1) finely to medium crystalline and (2) medium to coarsely crystalline. They commonly co-occur and show a gradual transition. Both exhibit breccia fabric under microscope. Dolomite texture reveals that the breccia fabric is not inherited from the precursor carbonates but was formed during the dolomitization process and under the influence of repeated seismic shocks. Dolomitization within the slope and basinal succession as well as within the breccia zones of the underlying basement block is interpreted as being related to fluid originated from the detachment zone and channelled along synsedimentary normal faults. The proposed conceptual model of dolomitization suggests that pervasive dolomitization occurred not only within and near the fault zones. Permeable beds have channelled the fluid towards the basin centre where the fluid was capable of partial dolomitization. The fluid inclusion data, compared with vitrinite reflectance and maturation data of organic matter, suggest that the ascending fluid was likely hydrothermal which cooled down via mixing with marine-derived pore fluid. Thermal gradient is considered as a potential driving force for fluid flow