On the volumes and affine types of trades

A $[t]$-trade is a pair $T=(T_+, T_-)$ of disjoint collections of subsets (blocks) of a $v$-set $V$ such that for every $0\le i\le t$, any $i$-subset of $V$ is included in the same number of blocks of $T_+$ and of $T_-$. It follows that $|T_+| = |T_-|$ and this common value is called the volume of $T$. If we restrict all the blocks to have the same size, we obtain the classical $t$-trades as a special case of $[t]$-trades. It is known that the minimum volume of a nonempty $[t]$-trade is $2^t$. Simple $[t]$-trades (i.e., those with no repeated blocks) correspond to a Boolean function of degree at most $v-t-1$. From the characterization of Kasami--Tokura of such functions with small number of ones, it is known that any simple $[t]$-trade of volume at most $2\cdot2^t$ belongs to one of two affine types, called Type\,(A) and Type\,(B) where Type\,(A) $[t]$-trades are known to exist. By considering the affine rank, we prove that $[t]$-trades of Type\,(B) do not exist. Further, we derive the spectrum of volumes of simple trades up to $2.5\cdot 2^t$, extending the known result for volumes less than $2\cdot 2^t$. We also give a characterization of "small" $[t]$-trades for $t=1,2$. Finally, an algorithm to produce $[t]$-trades for specified $t$, $v$ is given. The result of the implementation of the algorithm for $t\le4$, $v\le7$ is reported.Comment: 30 pages, final version, to appear in Electron. J. Combi

Online Bin Packing with Advice

We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log n + o(log n) bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n + o(n) bits of advice and achieves a competitive ratio of 4/3 + {\epsilon}. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.Comment: 19 pages, 1 figure (2 subfigures

On the List Update Problem with Advice

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than $15/14$. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of $2$ on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of $5/3$. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, TIMESTAMP and two members of the MTF2 family of algorithms. We also show that MTF2 algorithms are $2.5$-competitive

Reconstruction of aerodynamic angles from flight data for "slybird" Unmanned Aerial Vehicle (UAV)

The angle of attack and the sideslip angle are significant parameters describing the aerodynamics of the aircraft. Specifically, these angles are required for identification of the system parameters such as aerodynamic forces and moment derivatives. For exact measurements, it is necessary to install appropriate air data sensors on board. However, it is sometime difficult to install such apparatus on small UAVs. Inertial sensor measurements, aerodynamic derivatives and equations of motions are used to determine the aerodynamic angles. In this paper, three approaches are followed to estimate airflow angles. The first concept uses navigational equations for the estimation. In the second approach, inertial sensor data has been used. Third concept uses aerodynamic derivative obtained from wind tunnel testing. Estimated angles from all three approaches are shown for simulated and flight data. Complementary filter has been used for combining estimated angles obtained using inertial measurements and aerodynamic derivative based approaches. Improved filtered angles are compared with simulated airflow angles for the same flight condition

The People of Marutham Land: Their Lives and Culture

Social anthropologists have given various interpretations and definitions of culture. Culture is interwoven into the domestic as well as the public life of the people of the Sangam age. The culture of the people of Marutham land depended on agriculture. The people who lived in fertile agricultural lands lived by the disciplines that they could follow. Marriage is considered important and primary in Tamil culture. The Akananooru songs talk about the rituals of marriage. It is understood that "Silambu Kazhi Nonbu" (removal of anklets put on by the parents before the marriage of the girls) was the main ritual in the wedding rituals. The wedding rituals were simple. It is mentioned in the Kalitthokai that wearing new clothes at the time of the wedding, wearing new ornaments, adorning with garlands of flowers, and circumambulating the fire as guided by the Brahmin during the time of the wedding

Simultaneous Determination of Nitrite and Nitrate in Milk Samples by Ion Chromatography Method and Estimation of Dietary Intake

The presence of nitrate and nitrite in foods may be considered hazardous after ingestion in the gastrointestinal tract due to their reaction with naturally occurred secondary amines to form potentially carcinogenic nitrosamines. Due to this fact, a new method was developed in this study for the simultaneous determination of nitrite and nitrate in milk samples using by ion chromatography. Proposed mobile phase composed of sodium hydrogen carbonate and sodium carbonate (1.0 and 3.2 mmol/L) with a flow rate of 0.7 ml/min. The average recoveries for nitrate and nitrite were higher than 86 and 88, respectively. The limit of detection for nitrate and nitrite were 0.24 and 0.09 mg/L, respectively. The results of 102 real milk samples showed nitrate was found in all of the samples (100) with a mean of 34 ± 11 mg/L, while nitrite was found in none of the samples. The mean intake of nitrate in all age groups was lower than World Health Organization guideline. The present assessment concludes that the maximum contaminant level was equal to 82.8 mg/L nitrate. This method was fast, sensitive and accurate and is capable of being an alternative method in food control laboratories for investigation of nitrite and nitrate content. This is the first study of the determination and survey of nitrite and nitrate and exposure assessment of the Iranian population to nitrite and nitrate level in milk, which was widely used in infants and adolescents as one of the basic food components. Copyright © Taylor & Francis Group, LLC

Online Bin Packing with Advice

We consider the online bin packing problem under the advice complexity model where the "online constraint" is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log(n)+o(log(n)) bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n+o(n) bits of advice and achieves a competitive ratio of 4/3+e. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8

Real-time Measurement of Stress and Damage Evolution During Initial Lithiation of Crystalline Silicon

Crystalline to amorphous phase transformation during initial lithiation in (100) silicon-wafers is studied in an electrochemical cell with lithium metal as the counter and reference electrode. It is demonstrated that severe stress jumps across the phase boundary lead to fracture and damage, which is an essential consideration in designing silicon based anodes for lithium ion batteries. During initial lithiation, a moving phase boundary advances into the wafer starting from the surface facing the lithium electrode, transforming crystalline silicon into amorphous LixSi. The resulting biaxial compressive stress in the amorphous layer is measured in situ and it was observed to be ca. 0.5 GPa. HRTEM images reveal that the crystalline-amorphous phase boundary is very sharp, with a thickness of ~ 1 nm. Upon delithiation, the stress rapidly reverses, becomes tensile and the amorphous layer begins to deform plastically at around 0.5 GPa. With continued delithiation, the yield stress increases in magnitude, culminating in sudden fracture of the amorphous layer into micro-fragments and the cracks extend into the underlying crystalline silicon.Comment: 12 pages, 5 figure