A New Approximate Min-Max Theorem with Applications in Cryptography

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs

Modulus Computational Entropy

The so-called {\em leakage-chain rule} is a very important tool used in many security proofs. It gives an upper bound on the entropy loss of a random variable $X$ in case the adversary who having already learned some random variables $Z_{1},\ldots,Z_{\ell}$ correlated with $X$, obtains some further information $Z_{\ell+1}$ about $X$. Analogously to the information-theoretic case, one might expect that also for the \emph{computational} variants of entropy the loss depends only on the actual leakage, i.e. on $Z_{\ell+1}$. Surprisingly, Krenn et al.\ have shown recently that for the most commonly used definitions of computational entropy this holds only if the computational quality of the entropy deteriorates exponentially in $|(Z_{1},\ldots,Z_{\ell})|$. This means that the current standard definitions of computational entropy do not allow to fully capture leakage that occurred "in the past", which severely limits the applicability of this notion. As a remedy for this problem we propose a slightly stronger definition of the computational entropy, which we call the \emph{modulus computational entropy}, and use it as a technical tool that allows us to prove a desired chain rule that depends only on the actual leakage and not on its history. Moreover, we show that the modulus computational entropy unifies other,sometimes seemingly unrelated, notions already studied in the literature in the context of information leakage and chain rules. Our results indicate that the modulus entropy is, up to now, the weakest restriction that guarantees that the chain rule for the computational entropy works. As an example of application we demonstrate a few interesting cases where our restricted definition is fulfilled and the chain rule holds.Comment: Accepted at ICTS 201

Effects of Feeding a Finishing Diet Blended with Different Phases of Nursery Diets on Growth Performance and Economics of Nursery Pigs

A total of 1,260 weaned pigs (PIC TR4 × (Fast LW × PIC L02); initially 12.9 lb BW)) were housed in a commercial research barn and used in a 47-d study to determine the effects of blending a finishing diet into different phases of nursery diets on pig growth performance. Pens of pigs were blocked by initial BW and gender and allotted to 1 of 4 treatment groups (15 pens/treatment). In a 5-phase feeding program, the 4 treatments were: 1) standard nursery diets throughout (control); or standard nursery diets with 5.5 lb/pig of late finishing feed blended at the beginning of 2) Phase 2; 3) Phase 3; or 4) Phase 4. Phase changes were based on feed budgets. From d 0 to 7, all pigs received the same standard Phase 1 diet and had similar growth performance. Compared with pigs from control, blending finishing feed into the Phase 2 period resulted in poorer (P \u3c 0.01) ADG, ADFI, and F/G from d 7 to 14, poorer (P = 0.025) F/G from d 21 to 28, decreased (P = 0.028) ADG from d 28 to 35, and decreased (P \u3c 0.05) ADFI and F/G from d 35 to 47. Blending finishing feed during Phase 3 resulted in worsened (P \u3c 0.001) ADG and F/G from d 14 to 21, decreased (P = 0.010) ADG from d 21 to 28, and lower (P \u3c 0.05) ADFI and F/G from d 35 to 47 compared with control pigs. Pigs that received blended diet in Phase 4 had impaired (P \u3c 0.001) ADG and F/G from d 21 to 28, but had improved (P = 0.010) F/G from d 35 to 47. Overall (d 0 to 47), blending the finishing diet into Phase 2 decreased (P \u3c 0.05) ADG, ADFI, and final BW, but did not affect F/G compared with control pigs or pigs that had finishing feed blended into the Phase 4. Blending finishing feed into Phase 3 or 4 did not influence overall growth performance. Pigs that had finishing feed blended into Phase 2 or 3 had lower (P \u3c 0.05) overall feed costs than pigs from control and Phase 4 blending treatments. Gain value was decreased (P \u3c 0.05) when finishing feed was blended into Phase 2 compared with the control or when feed was blending into Phase 4. However, no differences in feed cost per lb of gain and only numerical differences in income over feed cost were observed among the treatments. In conclusion, feeding finishing feed in early nursery phase negatively affected pig growth performance; however, blending approximately 5.5 lb/pig finishing feed into nursery diets for pigs greater than 22 lb BW did not affect overall growth performance

Phosphorus requirements of grow-finish pigs raised in a commercial environment

We conducted three experiments to identify available phosphorus (aP) requirements of pigs reared in commercial facilities. In a pilot study (Exp. 1), 600 gilts (PIC, initially 95.2 lb) were randomly allotted to a low or high dietary P regimen in a 98-d study. Pigs were phase-fed six diets from 95 to 106, 106 to 150, 150 to 183, 183 to 212, 212 to 245, and 245 to 267 lb. Corresponding aP concentrations were: 0.30, 0.28, 0.27, 0.27, 0.24, and 0.19% (low) and 0.37, 0.33, 0.30, 0.28, 0.27, and 0.26% (high). No differences were observed (P \u3e 0.10) in ADG and overall F/G was greater (P\u3c0.07) for pigs fed the low aP regimen. In Exp. 2, 1,260 gilts (initially 74.5 lb) were randomly allotted to one of five dietary treatments in a 26-d study. Experimental diets contained 0.18, 0.22, 0.25, 0.29, or 0.32% aP, corresponding to 0.5, 0.6, 0.7, 0.8, or 0.9 g aP/Mcal ME. There were 28 pigs per pen and 9 pens per treatment. From d 0 to 14, increasing aP tended to increase (linear, P\u3c0.03) ADG and F/G (quadratic, P\u3c0.05) with the greatest response observed as aP increased from 0.18 to 0.22%. However, from d 0 to 26, no differences were observed for any growth traits (P\u3e0.12). Pooled bending moment of the femur, 6th rib, and 3rd and 4th metatarsals increased with increasing aP (linear, P\u3c0.01). Ash content of the rib and metatarsals numerically increased (P\u3e0.10) with increasing aP. In Exp. 3, 1,236 gilts (initially 195.1 lb) were randomly allotted to one of five dietary treatments in a 28-d study. Experimental diets contained 0.05, 0.10, 0.14, 0.19, 0.23% aP, equivalent to 0.152, 0.277, 0.402, 0.527, or 0.652 g aP/Mcal ME. From d 0 to 14, increasing aP increased (linear, P\u3c0.01) ADG and F/G. However, from d 0 to 28 increasing aP had no effect (P\u3e0.17) on growth performance. Increasing aP increased (linear, P\u3c0.05) bone ash and bending moment of the 3rd and 4th metacarpals. In commercial facilities, 74 to 121 lb pigs require approximately 0.22% aP to maximize ADG and F/G, whereas 195 to 240 lb pigs require approximately 0.19% aP. However, bone bending moment and ash continued to increase with increasing aP. These values correspond to 0.60 and 0.527 g aP/Mcal ME and 3.24 and 4.07 g/d of aP intake. Our results suggest percentage aP requirement estimates are similar to NRC (1998); however, because of the low feed intake of pigs in commercial facilities our study shows a lower requirement estimate on a g/d basis.; Swine Day, Manhattan, KS, November 14, 200

Evaluation of the effects of wheat gluten source and animal plasma blends on the growth performance of nursery pigs

A total of 472 weanling pigs (initially 13.5 lb) were used in two experiments to evaluate the effects of wheat gluten source (WG) and combinations with spray-dried animal plasma (SDAP) on growth performance of nursery pigs. In Exp. 1, the five dietary treatments included a control diet containing 6% SDAP, wheat gluten that was enzymatically hydrolyzed (Source 1), and a non-hydrolyzed wheat gluten (Source 2). The wheat gluten sources replaced L-lysine HCl and replaced 50% or 100% of the spray-dried animal plasma. From d 0 to 7, 7 to 14, and 0 to 21, increasing wheat gluten decreased (linear; P\u3c0.05) ADG. There were no differences between wheat gluten sources. Average daily feed intake decreased similar to ADG, with the exception that ADFI of pigs fed wheat gluten Source 2 had only a slight decreasing trend (P\u3c0.11) from d 0 to 7. Pigs fed the diet containing 6% SDAP had the greatest ADG and ADFI from d 0 to 21. When the SDAP was replaced with either wheat gluten source, ADG and ADFI linearly decreased (P\u3c0.01) but F/G improved (P\u3c0.04). When pigs were fed the common diet from d 21 to 35, there were no differences (P\u3c0.05) in ADG, ADFI or F/G. In Exp. 2, the six dietary treatments included a negative control with no SDAP or WG (0:0 ratio), 9% WG (100:0 ratio), 6.75% WG and 1.25% SDAP (75:25 ratio) combination, 4.5% WG and 2.5% SDAP (50:50 ratio) combination, 2.25% WG and 3.75% SDAP (25:75 ratio) combination, and a positive control with 5% SDAP (0:100 ratio). The wheat gluten (Source 1) was enzymatically hydrolyzed, but from a different lot than Exp. 1. From d 0 to 14, pigs fed 6% SDAP had numerically greater ADG and ADFI compared to pigs fed the negative control diet. However, replacing SDAP with increasing amounts of WG tended to decrease (P\u3c0.10) ADG and ADFI. These results confirm the improved ADG and ADFI of pigs fed SDAP immediately after weaning. In these experiments, replacing SDAP with WG resulted in decreased ADG.; Swine Day, Manhattan, KS, November 14, 200

Effects of Feeding Increasing Amounts of Finishing Diet Blended with Nursery Diets on Growth Performance and Economics of Nursery Pigs

A total of 1,260 pigs [PIC TR4 × (Fast LW × PIC L02); initial body weight (BW) 23.3 lb] were housed in two commercial research rooms and used in a 28-d study to determine the effects of blending increasing amounts of finishing feed into phase 3 nursery diets on pig growth performance. At weaning, pigs were placed into pens with 21 pigs per pen and 30 pens per room. Pigs were fed commercial nursery diets in a 5-phase feeding program with phases 1 and 2 fed before the start of the experiment. At the beginning of phase 3 (day 0), pens of pigs were blocked by pen weight and room. Within blocks, pens were allotted randomly to 1 of 4 treatments with 15 replications per treatment. Treatments consisted of a dose-titration of blending increasing amounts of late finishing feed (0, 2.75, 5.5, and 8.25 lb per pig, corresponding to 0, 3, 6, and 9 tons per 2,200-head barn, respectively) into a phase 3 nursery diet. Diet changes to the remaining phases were based on feed budgets. From day 0 to 14, average daily gain (ADG) was unaffected as finishing feed budget increased from 0 to 2.75 lb/pig but decreased thereafter (quadratic, P = 0.090). Average daily feed intake (ADFI) was unaffected, but feed-to-gain ratio (F/G) worsened (linear, P \u3c 0.001) as more finishing feed was blended into phase 3 nursery diet. From day 14 to 28, pigs previously fed increasing levels of late finishing feed had improved (linear, P \u3c 0.05) ADG and F/G, but unaffected ADFI. Overall (day 0 to 28), blending increasing amounts of finishing feed with phase 3 nursery diet decreased ADG (linear, P = 0.050) and tended to decrease (linear, P \u3c 0.07) ADFI and final BW. However, there was no evidence of any linear or quadratic effects of increasing finishing feed budgets on overall F/G. Feed cost, gain value, and feed cost per lb of gain decreased (linear, P \u3c 0.05) as finishing feed budget increased from 0 to 8.25 lb/pig. However, income over feed cost was not different among treatments. In conclusion, feeding increasing amounts of late finishing feed to phase 3 (28 lb) nursery pigs decreased overall ADG and ADFI, but did not affect income over feed cost

Effects of Increasing Soybean Meal in Corn-Wheat Midds-Based Diets on Growth Performance and Carcass Characteristics of Late Finishing Pigs

A total of 786 pigs (PIC TR4 × (Fast LW × PIC L02); initially 213.2 lb ± 2.37 lb) were used to evaluate the effects of increasing soybean meal (SBM) in corn-wheat middsbased diets on growth performance of late finishing pigs. Pens of pigs were blocked by BW and randomly assigned to 1 of 5 treatments with 9 replications per treatment. Experimental diets were corn-based with 30% wheat midds. Soybean meal levels increased from 0 to 16% replacing added feed grade AA. Pens of pigs were weighed to evaluate ADG, ADFI, and F/G. Data were analyzed with the GLIMMIX procedure of SAS and pen was considered as the experimental unit. The statistical model considered fixed effects of dietary treatment, linear, quadratic, and cubic contrasts, and random effects of block. Overall, final BW of pigs increased (linear, P \u3c 0.05) as dietary SBM increased. Additionally, overall ADG and F/G improved as SBM increased (linear and cubic; P \u3c 0.05) with no differences in overall ADFI. Although diets were formulated to exceed minimum NRC nutrient requirement estimates, we suspect that the increased Trp:Lys ratio in the 16% SBM diet may explain the cubic responses observed. These results suggest that corn-soybean meal-based diets with 30% wheat midds for late finishing pigs should contain at least 4% SBM

Effect of Sow Lactation Crate Size on Litter Performance and Survivability

A total of 529 litters of pigs (PIC TR4 × (Fast LW × PIC L02)) were used to examine the effect of sow lactation crate size on nursing pig litter performance and survivability. The sow portion of the farrowing crate was maintained at a constant length and width of 7.4 and 2.0 ft, respectively. To form the treatments, crate width was adjusted accordingly, taking space away from one sow’s crate to give it to another allowing for 3 crate widths: 4.8 (small), 5.4 (medium), and 6.0 ft (large). This allowed for blocks of 3 crates, where each treatment was represented. Sows were loaded into individual lactation crates at random, balancing for parity across treatments. Cross fostering occurred within 24 h of farrowing prior to obtaining d 1 litter weight in effort to equalize litter size across treatments. Data were analyzed using generalized mixed models where treatment was a fixed effect and block was a random effect. Born alive, piglets weaned, and pre-weaning mortality, were all fitted using a binomial distribution.Regardless of treatment, there was no evidence of differences in total piglets born (14.3), percentage of piglets born alive (92.3%), d 1 litter weight after cross fostering (40.0 lb), litter weaning weight (145.9 lb), litter ADG (5.4 lb/d), or number of piglets weaned (10.7). In addition, no evidence for differences was observed in the percentage piglets weaned (80.9%) or pre-weaning mortality (19.1%). In conclusion, increasing lactation crate size did not impact litter performance or pig survivability in this study

Effects of Dietary Corn Dried Distillers Grains with Solubles Withdrawal on Finishing Pig Performance and Carcass Characteristics

Two experiments were conducted to evaluate the effects of removing corn dried distillers grains with solubles (DDGS) at increasing intervals before harvest on finishing pig performance and carcass characteristics. For Exp. 1, 985 finishing pigs [initially 219 ± 5.5 lb body weight (BW)] were used in a 28-d growth study. There were 12 pens per treatment with 19 to 21 pigs per pen. There were four treatments decreasing in duration of withdrawal of DDGS from diets before final marketing: 28, 21, 14, or 0 d withdrawal. Regardless of treatment, pens of pigs were topped according to a typical summer marketing strategy with one top prior to final barn dump. All pens were topped by removing the 17% heaviest pigs on d -21 resulting in a final barn dump of approximately 83% of starting barn inventory. Overall, there was no evidence for effects of DDGS withdrawal time on final BW, average daily feed intake (ADFI), or feed efficiency (F/G; P \u3e 0.111); however, as withdrawal time increased, average daily gain (ADG) linearly increased (P = 0.022) and iodine value decreased (linear, P = 0.001). There was no evidence for treatment differences for hot carcass weight (HCW) or loin depth (P \u3e 0.106); however, dressing percentage was linearly increased (P = 0.001) with increased withdrawal time. Backfat depth was also decreased (quadratic; P = 0.019) and percentage lean increased (quadratic; P = 0.033) as DDGS withdrawal time increased. Feed cost and gain value were increased (linear, P \u3c 0.020) resulting in a marginally significant (P \u3c 0.100) increase in income over feed cost (IOFC) with increased withdrawal duration. In Exp. 2, 1,158 finishing pigs (initially 232 ± 4.3 lb BW) were used in a 35-d growth study. There were 15 pens per treatment with 17 to 21 pigs per pen. Similar to the first experiment, there were four treatments decreasing in duration of withdrawal of DDGS from diets before final marketing: 35, 28, 14, or 0 d withdrawal. All pens were topped according to a typical winter marketing strategy with two marketing events prior to the final barn dump. All pens were marketed by removing the 15% heaviest pigs on d -28, the 28% heaviest pigs on d -14, and a final barn dump of approximately 57% of starting barn inventory. There was no evidence that final BW, overall ADG, or overall F/G differed across treatments with increasing DDGS withdrawal times (P \u3e 0.116). Overall average daily feed intake increased (linear, P = 0.015) as time withdrawn from DDGS before final marketing increased. Iodine value decreased (P \u3c 0.022) and dressing percentage increased (linear; P = 0.034) with increasing withdrawal time. Lastly, feed cost and feed cost per lb of gain increased (linear, P \u3c 0.003) with increasing DDGS withdrawal time. In conclusion, these experiments demonstrate that longer feeding duration of DDGS before harvest decreases carcass yield and increases iodine value. Feed cost is reduced with longer feeding of DDGS, yet the gain value and IOFC responses varied depending on the marketing strategy

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral