Continuous glucose monitoring in an end-stage renal disease patient with diabetes receiving hemodialysis.

Diabetes is the leading cause of end-stage renal disease (ESRD) and contributes to heightened morbidity and mortality in dialysis patients. Given that ESRD patients are susceptible to hypoglycemia and hyperglycemia via multiple pathways, adequate glycemic monitoring and control is a cornerstone in diabetic kidney disease management. In ESRD, existing glycemic metrics such as glycated hemoglobin, self-monitored blood glucose, fructosamine, and glycated albumin have limitations in accuracy, convenience, and accessibility. In contrast, continuous glucose monitoring (CGM) provides automated, less invasive glucose measurements and more comprehensive glycemic data versus conventional metrics. Here, we report a 48-year-old male with ESRD due to diabetes receiving thrice-weekly hemodialysis who experienced decreased patient-burden, greater glucose monitoring adherence, improved glycemic parameters, and reduction in hypoglycemia after transitioning to CGM. Through this case, we discuss how CGM is a practical, convenient patient-centered tool that may improve metabolic outcomes and quality of life in ESRD patients with diabetes.

Better Circuits for Binary Polynomial Multiplication.

We develop a new and simple way to describe Karatsuba-like algorithms for multiplication of polynomials over F 2 . We restrict the search of small circuits to a class of circuits we call symmetric bilinear. These are circuits in which AND gates only compute functions of the form ∑ i ∈ S a i ⋅ ∑ i ∈ S b i (S ⊆ {0,…, n - 1}). These techniques yield improved recurrences for M(kn), the number of gates used in a circuit that multiplies two kn-term polynomials, for k = 4, 5, 6, and 7. We built and verified the circuits for n-term binary polynomial multiplication for values of n of practical interest. Circuits for n up to 100 are posted at http://cs-www.cs.yale.edu/homes/peralta/CircuitStuff/BinPolMult.tar.gz.

Improved upper bounds for the expected circuit complexity of dense systems of linear equations over GF(2).

Minimizing the Boolean circuit implementation of a given cryptographic function is an important issue. A number of papers [1], [2], [3], [4] only consider cancellation-free straight-line programs for producing small circuits over GF(2). Cancellation is allowed by the Boyar-Peralta (BP ) heuristic [5, 6]. This yields a valuable tool for practical applications such as building fast software and low-power circuits for cryptographic applications, e.g. AES [5, 7], HMAC-SHA-1 [8], PRESENT [9], GOST [9], and so on. However, the BP heuristic does not take into account the matrix density. In a dense linear system the rows can be computed by adding or removing a few elements from a "common path" that is "close" to almost all rows. The new heuristic described in this paper will merge the idea of "cancellation" and "common path". An extensive testing activity has been performed. Experimental results of the new and the BP heuristic were compared. They show that the Boyar-Peralta results are not optimal on dense systems.

Soil microbial community composition in tallgrass prairie restorations converge with remnants across a 27-year chronosequence.

Restoration and management of natural ecosystems is a critical strategy in mitigating global biodiversity loss. This is exemplified in the American Midwest by efforts aimed at reclaiming historical grasslands lost to high-yield agriculture. While restorations traditionally take the form of plant reintroduction and management, advances in microbial analyses suggest that soil communities could be indicators restoration success. However, current understanding of key microbial taxa and functional activities in both natural and restored ecosystems is limited. Here, we investigated the impact of nearly 30 years of carefully managed restoration on soil microbial communities at the Nachusa Grasslands in northern Illinois, USA. We characterized bacterial and archaeal communities in a chronosequence of restored tallgrass prairies ranging from 1 to 27 years old across a growing season and compared them to communities in pre-restoration agricultural fields and remnant prairies. Results indicate that older restorations harboured communities statistically distinct from newer restorations. These communities converged toward those in local prairie remnants, suggesting that plant-focussed restoration has yielded soil bacterial communities reflective of a successful restoration. Recovery of microbial clades within the Verrucomicrobia and Acidobacteria are an important feature of this convergence, and these groups could be targeted for future soil-focussed, bottom-up restoration studies.

Report on Pairing-based Cryptography.

This report summarizes study results on pairing-based cryptography. The main purpose of the study is to form NIST's position on standardizing and recommending pairing-based cryptography schemes currently published in research literature and standardized in other standard bodies. The report reviews the mathematical background of pairings. This includes topics such as pairing-friendly elliptic curves and how to compute various pairings. It includes a brief introduction to existing identity-based encryption (IBE) schemes and other cryptographic schemes using pairing technology. The report provides a complete study of the current status of standard activities on pairing-based cryptographic schemes. It explores different application scenarios for pairing-based cryptography schemes. As an important aspect of adopting pairing-based schemes, the report also considers the challenges inherent in validation testing of cryptographic algorithms and modules. Based on the study, the report suggests an approach for including pairing-based cryptography schemes in the NIST cryptographic toolkit. The report also outlines several questions that will require further study if this approach is followed.

The Interplay between Dietary Phosphorous, Protein Intake, and Mortality in a Prospective Hemodialysis Cohort.

(1) Background: Current dietary recommendations for dialysis patients suggest that high phosphorus diets may be associated with adverse outcomes such as hyperphosphatemia and death. However, there has been concern that excess dietary phosphorus restriction may occur at the expense of adequate dietary protein intake in this population. We hypothesized that higher dietary phosphorus intake is associated with higher mortality risk among a diverse cohort of hemodialysis patients. (2) Methods: Among 415 patients from the multi-center prospective Malnutrition, Diet, and Racial Disparities in Kidney Disease Study, we examined the associations of absolute dietary phosphorus intake (mg/day), ascertained by food frequency questionnaires, with all-cause mortality using multivariable Cox models. In the secondary analyses, we also examined the relationship between dietary phosphorus scaled to 1000 kcal of energy intake (mg/kcal) and dietary phosphorus-to-protein ratio (mg/g) with survival. (3) Results: In expanded case-mix + laboratory + nutrition adjusted analyses, the lowest tertile of dietary phosphorus intake was associated with higher mortality risk (ref: highest tertile): adjusted HR (aHR) (95% CI) 3.33 (1.75-6.33). In the analyses of dietary phosphorus scaled to 1000 kcal of energy intake, the lowest tertile of intake was associated with higher mortality risk compared to the highest tertile: aHR (95% CI) 1.74 (1.08, 2.80). Similarly, in analyses examining the association between dietary phosphorus-to-protein ratio, the lowest tertile of intake was associated with higher mortality risk compared to the highest tertile: aHR (95% CI) 1.67 (1.02-2.74). (4) Conclusions: A lower intake of dietary phosphorus was associated with higher mortality risk in a prospective hemodialysis cohort. Further studies are needed to clarify the relationship between specific sources of dietary phosphorus intake and mortality in this population.

Dialysis symptom index burden and symptom clusters in a prospective cohort of dialysis patients.

BACKGROUND: Dialysis patients experience a high symptom burden, which may adversely impact their quality of life. Whereas other specialties emphasize routine symptom assessment, symptom burden is not well-characterized in dialysis patients. We sought to examine the prevalence and severity of unpleasant symptoms in a prospective hemodialysis cohort. METHODS: Among 122 hemodialysis patients from the prospective Malnutrition, Diet, and Racial Disparities in Chronic Kidney Disease (CKD) study, CKD-associated symptoms were ascertained by the Dialysis Symptom Index, a validated survey assessing symptom burden/severity (with higher scores indicating greater symptom severity), over 6/2020-10/2020. We examined the presence of (1) individual symptoms and symptom severity scores, and (2) symptom clusters (defined as ≥ 2 related concurrent symptoms), as well as correlations with clinical characteristics. RESULTS: Symptom severity scores were higher among non-Hispanic White and Hispanic patients, whereas scores were lower in Black and Asian/Pacific Islander patients. In the overall cohort, the most common individual symptoms included feeling tired/lack of energy (71.3%), dry skin (61.5%), trouble falling asleep (44.3%), muscle cramps (42.6%), and itching (42.6%), with similar patterns observed across racial/ethnic groups. The most prevalent symptom clusters included feeling tired/lack of energy + trouble falling asleep (37.7%); trouble falling asleep + trouble staying asleep (34.4%); and feeling tired/lack of energy + trouble staying asleep (32.0%). Lower hemoglobin, iron stores, and dialysis adequacy correlated with higher individual and overall symptom severity scores. CONCLUSION: We observed a high prevalence of unpleasant symptoms and symptom clusters in a diverse hemodialysis cohort. Further studies are needed to identify targeted therapies that ameliorate symptom burden in CKD.

Boolean Functions with Multiplicative Complexity 3 and 4.

Multiplicative complexity (MC) is defined as the minimum number of AND gates required to implement a function with a circuit over the basis (AND, XOR, NOT). Boolean functions with MC 1 and 2 have been characterized in Fischer and Peralta (2002), and Find et al. (2017), respectively. In this work, we identify the affine equivalence classes for functions with MC 3 and 4. In order to achieve this, we utilize the notion of the dimension dim(f) of a Boolean function in relation to its linearity dimension, and provide a new lower bound suggesting that the multiplicative complexity of f is at least [dim(f)/2]. For MC 3, this implies that there are no equivalence classes other than those 24 identified in Çalik et al. (2018). Using the techniques from Çalik et al. and the new relation between the dimension and MC, we identify all 1277 equivalence classes having MC 4. We also provide a closed formula for the number of n-variable functions with MC 3 and 4. These results allow us to construct AND-optimal circuits for Boolean functions that have MC 4 or less, independent of the number of variables they are defined on.

Residual Urine Output and Mortality in a Prospective Hemodialysis Cohort.

INTRODUCTION: Although residual urine output (UOP) is associated with better survival and quality of life in dialysis patients, frequent measurement by 24-hour urine collection is burdensome. We thus sought to examine the association of patients' self-reported residual UOP, as an alternative proxy of measured residual UOP, with mortality risk in a prospective hemodialysis cohort study. METHODS: Among 670 hemodialysis patients from the prospective multicenter Malnutrition, Diet, and Racial Disparities in Kidney Disease study, we examined associations of residual UOP, ascertained by patient self-report, with all-cause mortality. Patients underwent protocolized surveys assessing presence and frequency of UOP (absent, every 1-3 days, >1 time per day) every 6 months from 2011 to 2015. We examined associations of baseline and time-varying UOP with mortality using Cox regression. RESULTS: In analyses of baseline UOP, absence of UOP was associated with higher mortality in expanded case-mix adjusted Cox models (ref: presence of UOP): hazard ratio (HR), 1.78 (95% confidence interval [CI], 1.16-2.72). In analyses examining baseline frequency of UOP, point estimates suggested a graded association between lower frequency of UOP and higher mortality, although estimates for UOP every 1 to 3 days did not reach statistical significance (reference: UOP >1 time per day): HR, 1.29 (95% CI, 0.82-2.05) and HR, 1.97 (95% CI, 1.24-3.12) for UOP every 1 to 3 days and absence of UOP, respectively. Similar findings were observed in analyses of time-varying UOP. CONCLUSION: In hemodialysis patients, there is a graded association between lower frequency of self-reported UOP and higher mortality. Further studies are needed to determine the clinical impact of more frequent assessment of residual UOP using self-reported methods.

Small Low-Depth Circuits for Cryptographic Applications.

We present techniques to obtain small circuits which also have low depth. The techniques apply to typical cryptographic functions, as these are often specified over the field GF (2), and they produce circuits containing only AND, XOR and XNOR gates. The emphasis is on the linear components (those portions containing no AND gates). A new heuristic, DCLO (for depth-constrained linear optimization), is used to create small linear circuits given depth constraints. DCLO is repeatedly used in a See-Saw method, alternating between optimizing the upper linear component and the lower linear component. The depth constraints specify both the depth at which each input arrives and restrictions on the depth for each output. We apply our techniques to cryptographic functions, obtaining new results for the S-Box of the Advanced Encryption Standard, for multiplication of binary polynomials, and for multiplication in finite fields. Additionally, we constructed a 16-bit S-Box using inversion in GF (216) which may be significantly smaller than alternatives.

Upper Bounds on the Multiplicative Complexity of Symmetric Boolean Functions.

A special metric of interest about Boolean functions is multiplicative complexity (MC): the minimum number of AND gates sufficient to implement a function with a Boolean circuit over the basis {XOR, AND, NOT}. In this paper we study the MC of symmetric Boolean functions, whose output is invariant upon reordering of the input variables. Based on the Hamming weight method from Muller and Preparata (1975), we introduce new techniques that yield circuits with fewer AND gates than upper bounded by Boyar et al. in 2000 and by Boyar and Peralta in 2008. We generate circuits for all such functions with up to 25 variables. As a special focus, we report concrete upper bounds for the MC of elementary symmetric functions ∑ k n and counting functions ∑ k n with up to n = 25 input variables. In particular, this allows us to answer two questions posed in 2008: both the elementary symmetric ∑ 4 8 and the counting ∑ 4 8 functions have MC 6. Furthermore, we show upper bounds for the maximum MC in the class of n-variable symmetric Boolean functions, for each n up to 132.

The Multiplicative Complexity of 6-variable Boolean Functions.

The multiplicative complexity of a Boolean function is the minimum number of two-input AND gates that are necessary and sufficient to implement the function over the basis (AND, XOR, NOT). Finding the multiplicative complexity of a given function is computationally intractable, even for functions with small number of inputs. Turan et al. [1] showed that n-variable Boolean functions can be implemented with at most n-1 AND gates for n ≤ 5. A counting argument can be used to show that, for n ≥ 7, there exist n-variable Boolean functions with multiplicative complexity of at least n. In this work, we propose a method to find the multiplicative complexity of Boolean functions by analyzing circuits with a particular number of AND gates and utilizing the affine equivalence of functions. We use this method to study the multiplicative complexity of 6-variable Boolean functions, and calculate the multiplicative complexities of all 150357 affine equivalence classes. We show that any 6-variable Boolean function can be implemented using at most 6 AND gates. Additionally, we exhibit specific 6-variable Boolean functions which have multiplicative complexity 6.

A Near-Optimal Algorithm to Count Occurrences of Subsequences of a Given Length.

For k ∈ ℤ+, define Σ k as the set of integers {0, 1, …, k - 1}. Given an integer n and a string t of length m ≥ n over Σ k , we count the number of times that each one of the kn distinct strings of length n over Σ k occurs as a subsequence of t. Our algorithm makes only one scan of t and solves the problem in time complexity mkn-1 and space complexity m + kn . These are very close to best possible.

On Various Nonlinearity Measures for Boolean Functions.

A necessary condition for the security of cryptographic functions is to be "sufficiently distant" from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that six common measures, nonlinearity, algebraic degree, annihilator immunity, algebraic thickness, normality, and multiplicative complexity, are incomparable in the sense that for each pair of measures, µ1, µ2, there exist functions f1, f2 with f1 being more nonlinear than f2 according to µ1, but less nonlinear according to µ2. We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions.

Microemulsions for Colorectal Cancer Treatments. General Considerations and Formulation of Methotrexate.

Microemulsions combine the advantages of emulsions with those of nanocarriers, overcoming the stability problems of the former and providing facile scalable systems with compartments adequate for high drug loadings. Recently, microemulsions are gaining attention in the formulation of anticancer drugs not only for topical treatment, but also for systemic delivery as well as for the development of theranostic systems. The aim of this paper is two-fold. First, an updated review about general features, preparation, characterization and pharmaceutical applications, with a special focus on colorectal cancer, is provided. Second, a case study of formulation of methotrexate in microemulsions is presented. Various essential oils (menthol, trans-anethole, α-tocopherol) and surfactants (TPGS-1000, Maxemul 6112, Noigen RN-20) were investigated for the preparation of o/w microemulsions for the delivery of methotrexate, and the ability of methotrexate-loaded microemulsions to inhibit cancer cell growth was then evaluated. Disregarding the surfactants used, menthol and trans-anethole led to cytotoxic microemulsions, whereas α-tocopherol based-formulations induced cell proliferation. These findings highlight the role that the oily component may play in the efficacy and safety of the microemulsions.