Background: Cardiotoxicity is an important and a common complication of cancer chemotherapeutic drugs. It may not only be associated with significant morbidity and mortality but also often becomes a limiting factor in adequate anti-cancer treatment. Several pharmacological agents are being evaluated for their efficacy in preventing cardiotoxicity of the cancer drugs.

Material and methods: Ninety patients with hematological malignancies undergoing chemotherapy and/or autologous hematopoietic stem cell transplantation (HSCT) were recruited in this study and were randomized to receive a combination of enalapril and cardvedilol (intervention arm) or no intervention (control arm). Comprehensive echocardiography and cardiac magnetic resonance imaging (MRI) were performed at baseline and at 6 months after randomization. The primary efficacy endpoint was the absolute change from baseline in left ventricular ejection fraction (LVEF).

Results: The mean age of the study subjects was 50 ± 13 years. By the end of the 6 months, there was a significant fall in LVEF in controls (3.28% absolute reduction from baseline) but no change was seen in the intervention group. As a result, at 6 months, LVEF was significantly lower in the control group in comparison to the intervention group (an absolute difference of 3.1% by echocardiography and 3.4% by cardiac MRI, p = 0.035 and 0.09, respectively). The beneficial effect was seen almost exclusively in patients receiving chemotherapy alone (absolute difference in LVEF of 6.38% at 6 months, p = 0.025) and not in those undergoing HSCT (absolute difference of 1.01%, p = 0.56). In addition, compared to controls, patients in the intervention group had a lower incidence of the combined event of death or heart failure (6.7% vs. 22%, p = 0.036) and of death, heart failure, or a final LVEF <45% (6.7% vs. 24.4%, p = 0.02).

Conclusions: The present trial showed that a combination of enalapril and carvedilol might prevent cardiotoxicity in patients undergoing chemotherapy for hematological malignancies.

Enalapril and carvedilol for preventing chemotherapy-induced left ventricular systolic dysfunction in patients with malignant hemopathies. The OVERCOME trial (preventiOn of left Ventricular dysfunction with Enalapril and caRvedilol in patients submitted to intensive ChemOtherapy for the treatment of Malignant hEmopathies)

An open-loop single-user multiple-input multiple-output (MIMO) communication scheme is considered where a transmitter, equipped with multiple antennas, encodes the data into independent streams all taken from the same linear code. The coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space-time code. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. It is shown that this communication architecture achieves the capacity of any Gaussian MIMO channel up to a gap that depends only on the number of transmit antennas.

Precoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap

An introduction to Diophantine Approximation. By J. W. S. Cassbls. Cambridge tracts in mathematics and mathematical physics, No. 45. Pp. 166. 22s. 6d. 1957. (Cambridge)

Let C be a nondegenerate planar curve and for a real, positive decreasing function ψ let C(ψ) denote the set of simultaneously ψ-approximable points lying on C. We show that C is of Khintchine type for divergence; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on C of C(ψ) is full. We also obtain the Hausdorff measure analogue of the divergent Khintchine type result. In the case that C is a rational quadric the convergence counterparts of the divergent results are also obtained. Furthermore, for functions ψ with lower order in a critical range we determine a general, exact formula for the Hausdorff dimension of C(ψ). These results constitute the first precise and general results in the theory of simultaneous Diophantine approximation on manifolds.

Diophantine approximation onplanar curves andthe distribution of rational points

Background Anthracyclines are a key chemotherapeutic agent used against hematological and solid organ malignancies. However, their benefits in cancer survival are limited by cumulative, dose‐relate...

Cardiotoxic Effect of Modern Anthracycline Dosing on Left Ventricular Ejection Fraction: A Systematic Review and Meta-Analysis of Placebo Arms From Randomized Controlled Trials

Let be a non-increasing function. A real number is said to be -Dirichlet improvable if it admits an improvement to Dirichlet’s theorem in the following sense: the system has a non-trivial integer solution for all large enough . Denote the collection of such points by . In this paper we prove that the Hausdorff measure of the complement (the set of -Dirichlet non-improvable numbers) obeys a zero-infinity law for a large class of dimension functions. Together with the Lebesgue measure-theoretic results established by Kleinbock and Wadleigh [A zero-one law for improvements to Dirichlet’s theorem. Proc. Amer. Math. Soc. 146 (2018), 1833–1844], our results contribute to building a complete metric theory for the set of Dirichlet non-improvable numbers.

Hausdorff measure of sets of dirichlet non-improvable numbers

© 2019 Cambridge University Press Let be a non-decreasing function, the the partial quotient of and the denominator of the the convergent. The set of -Dirichlet non-improvable numbers, \unicode[STIX]{x1D6F9}(q_{n}(x))\text{ for infinitely many }n\in \mathbb{N}\},\end{eqnarray}]]> is related with the classical set of -approximable numbers in the sense that. Both of these sets enjoy the same -dimensional Hausdorff measure criterion for. We prove that the set is uncountable by proving that its Hausdorff dimension is the same as that for the sets and. This gives an affirmative answer to a question raised by Hussain etA al [Hausdorff measure of sets of Dirichlet non-improvable numbers. MathematikaA 64(2) (2018), 502-518].

The sets of Dirichlet non-improvable numbers versus well-approximable numbers

Background
Anthracyclines are commonly used chemotherapeutic medications. In the current analysis we evaluated all-cause mortality and incidence, timing and response to medical therapy of anthracycline cardiotoxicity.

Methods
Left ventricular ejection fraction (LVEF) was serially assessed using gated heart pool scan/echocardiography in patients receiving anthracycline based chemotherapy from January 2009 to December 2014.

Results
A total of 1204 patients were administered anthracyclines during the study period. During a median follow up of 32 (IQR: 15 – 58) months, all-cause mortality was 38% (n = 463) with the incidence of cardiotoxicity 10.2% (n = 123). Only 15.4% (n = 19) patients required heart failure hospitalization with 48% (n = 59) of patients commenced on beta blockade therapy and/or angiotensin converting enzyme inhibitors. The majority of patients (73.2%, n = 90) experienced cardiotoxicity within 1 year of anthracycline initiation. The proportion of patients with complete, partial and no LVEF recovery were 16.3% (n = 20), 29.3% (n = 36) and 54.4% (n = 67) respectively. Mortality was higher in the cardiotoxicity group (49% vs 37%, p < 0.01). History of coronary artery disease, leukaemia, idarubicin use and high cumulative anthracycline dose were predictors of cardiotoxicity.

Conclusions
Cardiotoxicity after anthracycline use predictably occurs within first year of therapy and is dose related, with variable degrees of recovery. While the need for hospitalisation for heart failure was uncommon, medical therapy appears underutilised, suggesting there may be a role for improved surveillance and early initiation of treatment.

Incidence, time of occurrence and response to heart failure therapy in patients with anthracycline cardiotoxicity

Let $\psi:\mathbb R_+\to\mathbb R_+$ be a non-increasing function. A real number $x$ is said to be $\psi$-Dirichlet improvable if the system $$|qx-p|< \, \psi(t) \ \ {\text{and}} \ \ |q|<t$$ has a non-trivial integer solution for all large enough $t$. Denote the collection of such points by $D(\psi)$. Hussain-Kleinbock-Wadleigh-Wang (2018) proved the Hausdorff measure of the set $D^c(\psi)$ (the set of $\psi$-Dirichlet non-improvable numbers) by showing that it obeys a zero-infinity law for a large class of (essentially sub-linear) dimension functions. In this paper, we prove the generalised Hausdorff $f$-measure of the set $D^c(\psi)$ for non essentially sub-linear dimension functions. Hence, together with the Hussain-Kleinbock-Wadleigh-Wang (2018) result, we provide a complete characterisation of the generalised Hausdorff $f$-measure of the set $D^c(\psi)$.

The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers.

In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine–Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximation function.

Metrical results on systems of small linear forms

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