Minimal Representations of a Face of a Convex Polyhedron and Some Applications

In this paper, we propose a method for determining all minimal representations of a face of a polyhedron defined by a system of linear inequalities. Main difficulties for determining prime and minimal representations of a face are that the deletion of one redundant constraint can change the redundancy of other constraints and the number of descriptor index pairs for the face can be huge. To reduce computational efforts in finding all minimal representations of a face, we prove and use properties that deleting strongly redundant constraints does not change the redundancy of other constraints and all minimal representations of a face can be found only in the set of all prime representations of the face corresponding to the maximal descriptor index set for it. The proposed method is based on a top-down search strategy, is easy to implement, and has many computational advantages. Based on minimal representations of a face, a reduction of degeneracy degrees of the face and ideas to improve some known methods for finding all maximal efficient faces in multiple objective linear programming are presented. Numerical examples are given to illustrate the method.

Analiza krótko- i długookresowych związków pomiędzy giełdami azjatyckimi a rynkiem europejskim i amerykańskim

The aim of the article is to assess the relations between the Chinese and Japanese stock exchanges in relation to the American and European markets represented by the German market and to assess the impact of price fluctuations of the S&P500 and DAX indices on Asian stock exchange indices. In the study, the ADF test was used, according to which the degree of integration of the studied processes was determined and an appropriate class of distributed lag models and error correction was selected for the assessment of short- and long-term dependencies. The results of the conducted analysis clearly indicate that Asian exchanges are linked to both the American and German markets, but only in the case of index pairs NI225-DAX and SSEC-SP500 was the co-integration of processes confirmed, i.e. their joint pursuit of a long-term balance. In the case of the remaining pairs, co-in-tegration has not been confirmed, which means that there is a spurious correlation and therefore, a correct analysis of the mutual relations in these cases allows only short-term relationships to be detected. The results of the article may be helpful in choosing an investment strategy on Asian ex-changes adapted to its time horizon.

The 16 April 2016 Ecuador Earthquake Damage Assessment Survey

A damage assessment survey of 169 low-rise reinforced concrete buildings was conducted following the 16 April 2016 Ecuador earthquake. Forty-four percent of the buildings surveyed sustained severe structural damage. Using the collected data, seismic vulnerability indices were calculated to examine their correlation with damage observations. It was found that 92% of the buildings with observed severe structural damage had calculated wall and column index pairs (WI, CI) that satisfied the relation WI+CI/2 < 0.2%. The frequency of damage was lower for higher-priority index values, defined as the sum of CI+WI. Furthermore, frequency of damage in buildings with captive columns was observed to decrease with window height-to-column height ratios of more than 20%.

Causality between stock market and “fear gauge” indices: An empirical analysis with E-statistics

This study investigates empirically the validity of three hypotheses that have been advanced to explain the tendency of stock market and volatility indices to move in opposite directions, using the notion of Brownian distance correlation. We consider three stock market-implied volatility index pairs, namely, the S&P 500 and the VIX, the DAX 100 and the V1XI, and the N225 and the JNIV. The empirical results support the leverage hypothesis relative to the volatility feedback hypothesis for the pairs S&P 500 and VIX, and N225 and JNIV, and the representativeness and affect heuristics hypothesis relative to the leverage hypothesis for the pairs DAX 100 and V1XI, and N225 and JNIV.

Breeding ecology and predictors of nest success in the Critically Endangered Ridgway’s HawkButeo ridgwayi

SummaryRidgway’s HawkButeo ridgwayiis a Critically Endangered forest raptor endemic to the island of Hispaniola in the Caribbean. The species is currently limited to a small area on the north-east coast of the island, with fewer than 110 pairs remaining. From 2005 to 2009 we studied its breeding ecology, finding that Ridgway’s Hawks have a clutch size (2.0 ± 0.4 eggs) similar to other tropical raptors and islandButeospecies. Fledging rate of 0.64 fledglings per active nest (fledgling nest-1) with pairs raising a single brood per year was also similar to that of other tropicalButeospecies. Nest success was 40% (n= 151), with the majority of nest failures caused by human disturbance. The two significant predictors of nest success and fledging rate were related to human persecution: nest height and territory disturbance index. Pairs were able to tolerate human activity in their territory if there was no direct disturbance to the immediate nest area. Conservation planning for Ridgway’s Hawk must focus on community awareness programmes targeting local user groups within Los Haitises National Park regarding the uniqueness and endangered status of the hawk, and effective protection of the remaining karst forest in Los Haitises.